We stayed here for 10 days, sounds like what you’re after, right in the centre of town with parking outside (but they didnt really want bikes insdie). Previously we’ve used cheap motels. Going again for Outerbike this year.
http://kokopellilodge.com/kokopelli-inn-towner
Weather should be ok in may, but heating up. But it’s not like you’ll be doing 1000m climbs there.
There’s a few trails you can do from town – Pipedream, Slickrock, Amasa Back, Poison Spider / Portal Rim (but a bit more road). Shuttles are easy to arrange from any bike shop though.
I would recommend Whole Enchilada as a must-do, assuming the snow has cleared from Burro Pass (which it might not have in May). Mag 7 is a good shuttled trail too, and you can ride back to town via the Bar-M trails and new bike path.
I used the same site as sweaman for all my info on the newer trails.
I wouldnt worry about tyres, the usual shape and colour will do fine. If you’re are 26″, you’ll be in the minority 😉
You’ll have an amazing time, enjoy the <4% pale ales, cheap food and a really friendly town.