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The state of New Hampshire is very forthcoming about its tax rates. The state website has a page that lists total tax per thousand of valuation per town; it's in a PDF file and I found it right away on my first trip to the NH.GOV (or something like that) site. I printed it out and it made my work very easy when it came to choosing a place to live. It's under the Dept of Revenue Administration. Some of the very lowest are Bartlett ($6.60); Bridgewater ($7.44); New Castle ($4.49 but houses are very expensive there and there are very few of them); Newington ($9.07); Rye ($8.66, on the coast, less expensive/exclusive than New Castle but still hard to get into); Sandwich ($9.48--our favorite, in the Lakes Region); Moultonborough ($6.71--our second favorite, also in the Lakes area); and Freedom ($9.90). Some of them have likely gone up--this is from the 2006 tax table, which I printed out when I started my search. Still, it will give you a good idea of how vastly different the rates can be. Berlin's, for instance, is $29.24/$1,000. Of course maybe they drastically reduced their's last year so be sure to check!
The government is also very open about ticks. The health dept website has cases of Lyme Disease listed by incidence according to each town so you can get a good idea of where they bite most often. The CDC has a good site too, but of course NH's is the most detailed.
We are coming from New York where we have lived the past four years, +/-. Our property tax in Washington state, where we lived before NY, was $12/$1000 of valuation. Like NH, WA has no personal income tax. Our taxes here are about $25/$27 per $1,000 and the state has an 8 percent income tax on top of that. It seems that in NY every agency levies its own tax and they just keep climbing. Our tax "burden" as I see it called on tax websites, went from $100/month to more than $1,000! Per month! "Cost of Living" never meant a single thing to me until we moved here and I found out how painful it can really be.
We love New Hampshire and can't sell this house fast enough to get there. I've never been to Kentucky but in my opinion New Hampshire has more going for it than most states in the USA. Not too many people, not too many taxes, Dartmouth College, lakes, mountains and a lovely 12-mile strip of ocean.
I agree with you about how easy it is to find the equalized tax rates for all towns in NH.
I will caution you that several of the towns you mentioned have had an incrase in tax rates since 2006.
2008 total tax rates:
Bartlett= 8.11
Bridgewater= 8.14
New Castle= 4.68
Newington= 8.97
Rye= 9.62
Sandwich= 10.90
Moultonborough= 7.66
Freedom= 9.90