I live in downtown New Haven. I know for some of the games, your options are pretty limited, but for ESPN, everyone should have it.
Liffey's would be my first choice, but it is a soccer bar first, and a sports bar second, and there will be Premier League games on at that time and a bunch of soccer fans, so it might not be super fun. I haven't watched games at Archie Moore's really, and it's not downtown, but should be a solid option. Cask Republic will have the games on but their TV's are kind of crap.
The new Tavern has a giant television and will almost certainly show the game and has an open air bar, but it's not a particularly good bar -- where Black Bear used to be. But it's not bad. Kelly's is another option.
The Trinity is another option but again, as an Irish pub, they tend to show soccer very early.
I'd probably go:
1. Archie Moore's
2. Kelly's/Tavern
3. Liffey's (only cause of soccer)
4. Trinity