At the moment, the interest in UConn from other New England states is less than the interest in U of Michigan by Upper Peninsula residents, but more than the interest in University of Indiana by Illinois residents.
UConn has a program for reduced tuition and preferential admission for students from other New England states, so it is in some ways like a secondary state school to other New Englanders, but awareness of this and marketing of it has been minimal; this could be played up. Also, UConn men's and women's basketball has gotten a lot of traction among New England residents. If you saw ESPN's fan maps during the men's tourney, UConn dominated New England and New York during the NCAA tourney, but lost the rest of the country. Football, not yet, but that would probably change if B1G schools were coming to New England.
There is a lot of room for growth. Not much college sports presence in New England or New York. UConn is by far the top school but there is still a lot of room to capture more attention.
This is a good post to answer the OP's question. In addition, I would add that UCONN gets a fair amount of attention from Boston media (The Boston Globe, Herald, etc). Boston considers itself the "hub" of New England and their coverage includes most/all New England schools and teams. UCONN, I'd say, is featured more often than other New England schools simply because of the success UCONN has had in the college sport that most people in New England care most about: basketball.
College football has a ways to go in New England but as pj mentioned here, it would absolutely stick with a B1G schedule. UCONN fans have grown up watching other schools' football programs and, thanks to Penn State, we have seen a fair amount of B1G football. You bring those same schools to Connecticut and sellouts and stadium expansions would not be an issue whatsoever. It's a much tougher sell to a UCONN fan that they need to go watch Memphis or Tulsa. Boston College is too small and too private to capture all of New England. As Fishy said above, they capture a VERY small sliver of Boston. If you hop on the T and go to BU or Northeastern, the hate for BC is quite strong thanks to their hockey rivalries. In addition, BC doesn't have a strong of a local alumni connection that UCONN has. Again, because of it being a private Catholic affiliated school, their students come from all over. A fair amount of them leave the area post-graduation. Because of UCONN's reduced tuition for New England states, as pj said above, there is a very strong UCONN alumni base in the northeast that stays in the northeast. And if you ever want a peek at what Boston College vs UCONN basketball games were like at Conte Forum, google up a game and admire the 50% UCONN fans in attendance. It's one of the reasons why they want nothing to do with UCONN being on level-footing as they are: they know that UCONN fans will soon take over their Alumni Field too. "Protecting their turf" (their "turf" is the 3 block radius that Fishy mentioned).
As for RU and NYC: yes, there is quite a wave of excitement here in July about RU adding cable boxes. That is, after all, the reason why RU was invited into the B1G: cable boxes. For the B1G alumni living in NYC, this is great. But if you are expecting any bit of excitement from RU as an athletic department, I'm afraid you will be waiting quite a while. UCONN, in our short 10 year history, has had as much success and tradition as Rutgers has in 150 years. And if you think Rutgers is a gateway into MSG, then you're also sorely mistaken. Rutgers fans don't get a hoot about basketball and rightfully so...they are hideous. NYC is a college hoops town, thanks to its very strong Big East roots. There are two schools that capture NYC during Tourney Time: the fruit school from Upstate New York and UCONN. Case in point: the Big East Final between Providence and Creighton drew 15,000 fans (3,000 short of a sellout). UCONN in the Regional Finals set records for ticket prices on the secondary markets and drove up prices that cost more than Final Four tickets. I was at the Michigan State/UCONN Elite 8 game and the atmosphere for that game was electric. There is NO way a Rutgers game...or any B1G game that doesn't involve UCONN (or Upstate New York Fruit)...can generate that same kind of atmosphere. So yes, RU has delivered in July. But if you're expecting them to deliver anything whatsoever come December/January or March/April, I would suggest that you temper your expectations. NYC is a package deal: Rutgers and UCONN captures it and locks out the ACC in all phases. Cable boxes and "big game buzz" (not to mention, part of the NYC DMA is located in Connecticut and UCONN Country). You need both to capture NYC.
To sum, UCONN has presence in the #1 DMA, #7 and all of #30. We deliver cable boxes AND big games. Nobody else in the New England and tri-state area can do that.