I was looking at the other answers and would also recommend Lakes Region, around Lake Winnipesaukee. This is located in Central New Hampshire and is a vacation destination to so many. Although not close to the city for access to museums, etc., you are about an hour away from Concord/Manchester and two hours to Boston. We have many activities all through the year and there is always something to do. As far as taxes, Moultonborough is only $8.61/thousand, Center Harbor is $10.96/thousand, and Meredith (super cute town) is $12.51 per thousand...so not bad. Also, the property values maintain their value, as this area is highly desirable.
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I myself love Durham in the summer, but tend to avoid it in the winter with the increase in traffic and noise when the college kids come back to town.
There are many nice areas of NH. Scott I can certainly show you all of them for you to look at and pnder any pros and cons of each.
Although Manchester is a very good option, Portsmouth is Great. Everything you have mentioned in your wish list fits perfectly there as well as Manchester but, has the Seacoast appeal!
I'd be happy to send you along some information if you would like, you can reach me at 603-488-6272 and email firstname.lastname@example.org