Hello, I just posted a reply on a similar thread but yours is rather newer! We relocated to MK from London last year when I was pregnant. We live in Bradwell Village and really like it. It's easy cycling distance to the station, or about a 25-minute walk, it's just over a mile. My husband usually cycles, there are plenty of racks at the station, and so far no thefts! Fast trains to London are half an hour and go so regularly I don't even bother checking the timetable. In the evenings you only get slow trains though, so it takes an hour after about 9 pm.
The whole city has "redways" which are for pedestrians & cycles only. These are all great for walking with the pram, and you get into open greenery quite quickly even living so close to the centre. I do of course use the car almost every day, because it's just a lot easier for shopping. There's an Ikea in Bletchley, which has proved very handy. The only snag for us is that living close to the station means we're not that close to the M1 junction - it's on the Eastern side of the city, only takes about 10 minutes though, so not disastrous.
Other good parts of MK and surrounding area, in my opinion (not that I know a great deal) are: Shenley, Stony Stratford, Woburn Sands, Olney, Willen, Middleton. These are however all further away from the train station and would all be driving distance.
Generally speaking you will find some pretty dodgy estates close to the city centre; I would definitely avoid Lakes, Conniburrow, Heelands, Coffee Hall, Netherfield. Wolverton is further away, but also not very nice. You do get a feel for what won't work for you pretty quickly.
Most estates in MK are of course new build; Bradwell Village is ancient but has been extended with some rather ugly bungalows. What you'll find quite odd here is that there'll usually be a clutch of pretty houses on a nice estate, surrounded by some sort of dodginess. It just takes a bit of getting used to, and so far nothing has turned out to be that scary after all.
Prices are amazing in terms of what you get for your money, so for 350 you'll likely be able to get a good 4-bed family home.
anyway, hope that helps! If you do move here, happy to have a coffee as the big drawback for me is that I've met absolutely no one (I'm basically crap at going to things).