I have 3 children and have hosted 16 birthday parties in the last 8 years.
For us a village hall with bouncy castle party has always worked very well at 3 and 4 yrs and is very straightforward to organise with no mess at home.
We usually do a 2 hour party 2-4pm.
Aim for party food at about 3.15pm.
Play music it adds to the atmosphere - make up a 2 hour playlist of jolly pop songs with acceptable lyrics.
As well as the bouncy castle do an optional - 'pin the tail' but bear in mind most of the children won't want to wear a blindfold so have one for those who do otherwise they can close their eyes. Every child gets a small bag of haribo (or whatever you prefer) for taking part. No overall winner, just let them have the fun of seeing where their try ended up. Start this at about 2.30pm. They'll come in dribs and drabs but usually everyone ends up with a turn. It's a calm but fun activity, games that involve running around or someone being out don't go down well with 3 year olds ime.
Don't scatter balloons around lots of children are scared of the bang if they burst.
Don't do a pass the parcel if you have more than about 8 kids - they get bored.
Don't bother with sandwiches - you aren't feeding them lunch just an afternoon snack really. I do mini sausages, mini sausage rolls, pom bears/hula hoops/wotsits, sliced grapes, cheese cubes, sliced cucumber, party ring biscuits, chocolate fingers, that sort of stuff and sometimes I make fairy cakes depending on how much time I have. Put it all out on the table at the same time - who cares if they only eat the biscuits?!
Birthday cake and 'happy birthday when they mostly look like they've finished eating.
If you have enough family/friends helping you out make tea/coffee for the parents and hand round a box of biscuits. Village halls always have a tea urn and crockery you can use.
Hand out party bags with slice of birthday cake from 3.45pm. It's a signal for people to leave!
Two hours will fly past!