There are about six DSLAMs around Grafton. Before we moved here, I drove around to find all of them. The closer you are to a DSLAM, the better your speeds, up to 15 Mbps. FairPoint is the only provider. I'd be happy to point them out to you if you visit Grafton.
In the graphs below, WAN 1 is our DSL connection and WAN 3 is our LTE connection.
Verizon 4G LTE is available at our home in the northwest corner of town, but only because we're up on a hill with line of sight to Whaleback Mountain. With a grandfathered unlimited data account, it might be worth it, but even in the best of conditions, LTE really is still a "mobile" technology. DSL is rock solid, but LTE service is very inconsistent in comparison.
In our house, we have a Wilson Electronics LTE (700 MHz) antenna and repeater/amplifier, with the directional antenna pointed directly at the Verizon tower, so this is with the best possible conditions.
There are no cable providers in Grafton (to my knowledge).
T-Mobile service is not available (data or voice) anywhere in Grafton. T-Mobile 3G service is available on Route 4 until about Barker Steel in Canaan.
When we first moved here, we had several guests with AT&T phones and they were able to get service at our house, but recently (within the last six months) AT&T folks who were visiting were not able to get any service. Not even texts.