Manchester and Nashua will have the most diversity in a state that doesn't have a lot - they are the 2 largest cities NH has!
There is no state income tax or general sales tax (except prepared food), so that helps to compensate for the real estate tax. Seriously, sinceyou're coming such a long way and from such a different climate, you'd be much better off renting for a year while you explore the area and decide where you want to buy (if you still want to buy after you've been through a complete winter). Diversity may not be all its cracked up to be, and you may decide that some of the other, smaller towns surrounding, are better. Or not. But renting first gives you the option to see what you like before being locked in. In any case, you might want to look around
Northern New England Real Estate Network - Official Website of the Northern New England MLS to see what housing costs are and what the last taxes were. ValC is a gem and you can't go wrong with her.