I recommend the Eagle F1 All Seasons. they handle nearly as well as a good number of summer tires, mostly ignore water, and also handle the winter weather quite nicely. I only got stuck with these tires once this last winter...
and it had nothing to do with the tread of the tire, either.
The Eagle F1 AS tires have a treadwear of 400, which means they should easily last 20,000 + miles.
If you don't have to deal with light snow, or if you intend to swap out your tires for a true winter tire, this might not be the tire for you. I've been very happy with mine so far. I paid 125 per tire at the tirerack (which is going to put you over your budget)
Looks like they come in the size you specified, but they're currently 155 a tire.
