I'm going to jump in if I can being I'm a Sox fan and make 4 to 6 trips to Fenway per season. Have been there for a decent amount of matchups with NY. Pavilion seats aren't bad but I tend to sit and prefer the loge or field boxes. The Sox ticket office holds between 200 to 300 gameday tickets for sale if you don't want to go on the secondary market looking for them but the line forms early and gets long very quickly. If you go the secondary route, ace tickets is your go to place. Office is right around the corner from the park. If you want to check out seats and if there is any obstructions in the way, go to
www.preciseseating.com. It shows you the view from every seat in the park. I've been to weekend and weeknight games. Which you end up deciding on is personal preference. I always stay at the Marriott Copley and it's a 10-15 minute walk. That place sells out quickly so alternatives are the Hilton or Westin. Mandarin Oriental on Boylston if you want to go all out and splurge and If you want very basic lodging, there is a HoJo 1 block away on the Van Ness St (1st base side) of Fenway.
As someone mentioned, if you go up for a weeknight game, hit the Sam Adams brewery tour. 2 buck donation is your entry fee. Sam Adams is closed on the weekends but you can check out the Harpoon Brewery which is over by the waterfront. Your place to dine is Atlantic Fish company. Also on Boyleston. Their Saturday night dish is Lobster Thermadour. You can see it for yourself if you find yourself over there.
I'm biased but I love the park and I'll take it any day over any of the new bells and whistles places. The rivalry has changed among the fanbases since 2004 and as long as your respectable and not an arrogant douche, no one will give you a hard time even if you're wearing the opposing teams attire.
One other thing I forgot to mention, Boston like a previous poster said is very walkable if you decide to stay in the Back Bay Area. If you plan to move around, take the T. Piece of cake. NYC has numbers and letters to identify lines, Boston uses colors. Red is the one that takes you across the Charles to Harvard and MIT, Green takes you to Fenway, Silver takes you out to Logan. Buy a Charlie card during your stay and use that. It's Boston's version of the Metro Card.