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Steve F Wait, One more reply here... Yes, you'll have plenty of time. Besides, some of the older folks arrive after the game's begun to avoid the mass of Fenway rabble. Some hang in the bleachers after the last pitch to soak up the aura. To me, it's even more wonderful when empty. Some excellent suggestions above, so whatever the choice you'll have a fun memory. How I'd do it...
Short, free shuttle from the terminal to the Airport 'T' station then two subway stops to Aquarium Station. Walk across Atlantic Ave to the Marriott Long Wharf our long-time favorite (not too cheap, but certainly memorable). Why here?, Great skyline view, on Columbus Park at the waterfront and the newly designed Kennedy Parkway, close to several clubs and Revolution-era pubs, evening blues cruise and whale watch, Quincy Mkt shopping, powerful history, antique structures and the neighboring North End has the best grub east of Mulberry Street. Added bonuses, the harbor seals play in the pool outside the Aquarium 24/7 and the old Goudey Gum Company headquarters still stands across the street. Don't bother dumpster diving though 
Game time shortly? We always walk but you won't have time; From the Marriott, walk through Fanuel Hall (Stop at Pizzaria Regina for a couple of slices) to the Government Ctr 'T' station and catch the green-line to Kenmore Station. NOT Fenway Station. Yes Yanks fans... This was a scheme of old Mayor Curley, to piss you guys off 
Fill up on cheap beer at the Cask'n Flagon up the hill to the park or, if you're early enough the Bleacher Bar. It has a great view of the field and literally in the belly of the Green Monster.
You likely won't have time pre-game, but afterwards walk over to McGreevy's Third Base Saloon on Boylston St, it's on the way back anyway. Tons of stunning vintage Boston American's memorabilia is displayed and you may be served by Nuf Ced's great granddaughter.
Regardless of how you go, wear sneakers. We always walk back home to the Marriott from Fenway, it's just a little over two miles... Down posh Newbury St, across the Public Gardens and a pit stop at Cheer's, aka The Bull 'n Finch pub. It can be touristy but the place is actually pretty good and reasonable. Heading back, through the Common, by the Granary Buryng Grounds; Samuel Adams, John Hancock, Robert Treat Paine, Peter Faneuil, Paul Revere; James Otis, Mother Goose and five victims of the Boston Massacre and I'm not talking 2004 WSC 
... Continue down State St to the harbor, stopping near the hotel for a couple more and some pub grub at Kitty O'Sheas or An Tain.
If you're up to it, several of the Italian joints in the North End serve until late and just a short walk furthur.
Bear in mind, you can hop on the 'T' by McGreevy's, at Hynes Ctr station back to Government Ctr station, where the odyssey began. Boston's is a very safe, clean and simple four-line subway system.
Be aware, a scant number of Sox fans, but not all, can become instant Massho1es when etoh is added. Though most MLB team gear is ignored throughout the city, never wear any thing NYY in any bar. Sadly, the warning inside An Tain is not a joke. Funny thing, I didn't hear a peep from these 'devotees' from 1968-2004?
Option, I've always wanted to stay a night at the notorious Charles Street Jail, ca1851. Now, Boston's Liberty Hotel. Even though it's an archtectural Ugly Duckling story, thankfully, very little of this gothic, granite structure has changed but what has is stunning. But, though my granpa stayed there for nothing, rooms are now around $350 a night and it's located, on purpose no doubt, a wee bit too far from the waterfront.
Which game is it, seats? I often buy seats a 4-5 days early for cheap $ when there's an even chance of rain. Forecasts improve or worsen at the last minute here and I've fairly been lucky with the rain-outs.
Guaranteed you'll have a blast. Steve