I live in Lee purposefully for the school (we are in a co-op with Madbury and Durham). Housing is very competitive, although the top of your budget might be less competitive (if any houses in that range come on the market). Houses in my neighborhood are going for just over $500k, I had mine appraised 3 years ago during my divorce for $350k (and I bought it for $265k in 2013). It's a relatively easy jaunt to go to portsmouth, although you'll curse loudly during the commute home over the rt 4 bridge in Newington.

I cannot say enough good things about the Oyster River school district. I've known people that worked in both the Exeter and Portsmouth districts, and while those are pretty good, there are some institutional problems that make me doubly happy about Oyster River.

I used to live in Newmarket, and I think the school there is pretty good, it was lacking a bit for what we needed. so we decided to move about 9 years ago. I still live a 7 minute drive to downtown newmarket and can get my vanilla latte at crackskulls with a smile. Oddly enough, when I moved back to NH in the mid 2000's... there was a house for sale in Lee that we would have bought (this was pre-child) but we balked at the taxes. Now I'm glad to be here and can stomach paying a premium tax rate... wish I really thought that through then. would have saved a lot of headache.

Edit to add: Barrington has a tuition agreement with Oyster River where students can tuition into the high school. I think though it is competitive to get a spot, but I'm not 100% sure.