I have many years experience of living in Oak Park.
It is extremely safe.
I am talking doors unlocked, safe to walk around at night, incredibly responsive police if anything goes wrong (unfortunately the only thing that made OP unsafe for me was my exH). Kids ride bikes around, people go for walks, teens go to the movies, you can freely walk around without worry.
The Village and police work together to eliminate graffiti, which tends to be a toe in the door for gang activity. If you see some you can make a report to a hotline iirc. There is a Township Youth office that co-ordinates with the Police to form relationships between police and teens. Police hang out at public basketball courts. There is a youth curfew that is enforced for the most part.
The high school boasts many resources to boost student wellbeing - social workers and counsellors and deans of discipline working together to head off trouble. Again, there is co-operation with the police dept.
Oak Park is bordered by Roosevelt Road to the south, Austin Blvd to the east, Harlem Ave to the west and North Ave to the north. All are busy streets. North and Roosevelt are commercial corridors, Harlem is commercial in spots, and Austin is far less so.
The surrounding communities are Berwyn and Cicero (north western edge of Cicero) to the south, by River Forest and Forest Park to the west and west-south west respectively, and by Chicago to the east and north.
Berwyn is largely WC Hispanic along its north end that borders OP and is a safe municipality. Cicero has a bad reputation from its days as Al Capone's stomping ground, but it's very WC Hispanic now, and quiet.
Forest Park is safe (it's where OP goes to booze, has lots of bars and also lots of quirky shops and good restaurants along Madison Street). Forest Park is in a high school district that used to be one of the worst in the area but activists on its board managed to get a new Math and Science Academy built so it's becoming quite a hot place for property values. It used to be the place where you bought your first home, sent your children to RC elementary school, and then sold up to move to OPRF District 200 for high school. That is gradually changing. There are newer apartment and townhome developments and house prices are rising.
River Forest is quite UMC, mainly residential, and has a very low crime rate. West of River Forest is Maywood, separated from RF by a big area of woodland and the DesPlaines River. Maywood is a dire place. However, River Forest is incredibly safe. Again, very responsive police, plus the big nature preserve buffer. The community is very homogenously white and UMC whereas OP is a lot more diverse (still MC-UMC).
A little further west again is Melrose Park, home of Costco at North and 1st Avenue. Melrose Park is run by the Mafia but it's safe.
North of River Forest is Elmwood Park, again with strong Mafia links, but very safe. North of Oak Park across North Avenue is a neighbourhood of Chicago called Galewood. Two former governors of Illinois lived there before their election, one the notorious Rod Blagojevich and the other the fairly harmless Pat Quinn. It's a very MC part of Chicago.
The Austin neighbourhood of Chicago is the one next door to OP. It is plagued by violence and crime, gangs and drugs, but once you cross Austin Blvd to OP you are in a different world. I once walked home from West Suburban Hospital (situated on Austin) at 3am (long story - I had accompanied someone there in an ambulance and they were stable by 3) because I only lived a few blocks west and thought a taxi would be overkill. I encountered only bunny rabbits 
.
South of the Eisenhower (I-290) OP borders the Chicago neighbourhood known as 'The Island'. It's a quiet little enclave. Just north of the Eisenhower, from the highway to Jackson Blvd on the Chicago side is Columbus Park, again providing a buffer. The stretch of Austin from Jackson to North Avenue is the part of Austin where any overflow of problems from Chicago can be felt in OP.
All areas of OP are safe to live in.
If you wanted to be completely sure of your safety, don't live on the OP side of Austin Blvd itself, and probably avoid the first two-three blocks west of Austin. South of the Eisenhower you will find, in general, any street east of Lombard and anywhere a block north of Roosevelt Road will be very nice, and also quiet. Austin Blvd south of the Eisenhower has a lot of highway-related traffic. Austin is noisy and there can be a lot of sirens as there is a hospital on the OP side.
Apartments tend to be older in OP, walkup style (no lifts, stairs outside at the rear and inside in the front). Three floors is the norm. There are newer high rise apartment buildings too, some currently under construction. Washing machines in the older apartment buildings tend to be in the basement and you can expect to pay $1.50 per wash and the same for the dryer. Central AC is only available in new buildings.
Nearly all the streets have alleys running behind the houses/ apartments. This is where the wheelie bins are, and people set up basketball nets, older kids hang out to shoot hoops... Garages open onto the alleys.
Parking in OP is a true PITA unless your apartment comes with a dedicated spot, or your house has a parking bay or garage. Residents often rent out parking spots. Overnight street parking comes with a quarterly charge of $130 or so to the Village, and there are regs about when you have to shift your car, snow route parking - all available from the Village of Oak Park website.
OP has two local train 'El' lines (Blue running along the Eisenhower and Green following Lake Street) with several stops on each line, as well as a Metra (long distance commuter rail) stop at Harlem/North Blvd which serves OP and RF has a stop at Central Ave. The Metra is non-stop to Union Station, with the trip taking 20-25 mins, and a little longer if the train stops at Kedzie in Chicago. You can get some crazies on the El, but normal rush hour (to 9pm ish) and daytime travel is usually problem free. A trip downtown (depends on your stop) will take 40 - 45 mins or so, which is far better than a trip by car, especially as the Jane Byrne interchange is in a state of destruction/construction right now, and train is a lot cheaper too.
The Village strives to provide excellent services and by and large succeeds - leaf and snow removal and salting of streets are probably the biggest co-ordinated efforts you will see. But there are also the three excellent libraries (connected to the metropolitan area loan service) - the Main Library is fantastic but the Dole and Maze branches are wonderful smaller outposts serving north and south sides of the village respectively.
There are two public pools that are open all summer, and a year round rink. There are public tennis courts, a skate park, dog parks, basketball courts, a beach volleyball court, lovely neighbourhood parks/playgrounds, pitches for soccer (AYSO) and fields for T-ball, softball and baseball (OPYBS). Summer camps are offered by the Park District as well as multiple other schools and organisations. Sport is huge - many organisations offer coaching, organised leagues, etc. Music is also huge (Children's Chorus, School of Rock, public and private school bands, local orchestra that is very good indeed, excellent concerts held in local churches, Fitzgerald's Bar on Roosevelt in Berwyn holds sold out music fests and concerts by big names, lots of people living in OP are members of the Chicago Symphony Orchestra...) Drama is really big too, and you honestly couldn't throw a brick without hitting someone coming from or going to a dance class. Or yoga. OP is yoga central..
People are friendly - your neighbours will introduce themselves and you will be expected to tell your life story, hang out, go to the block party, take part in Hallowe'en, decorate your house for various holidays, chat. People give neighbours their keys, shovel snow for older people, lend a ladder or a particular tool, or a helping hand if you're having car trouble.
There are lots and lots of friendly teens to babysit.