Any game that is on SNY is blacked out on ESPN3 in areas that offer SNY on their cable systems. You'll be able to watch it on replay right after the game is over however.
Slingbox allows you to watch shows from your cable source at home while anywhere in the world. To watch UConn games that are blacked out you would need to put the box somewhere where the game is available and then connect to it from your home.
I've been toying with the idea of getting rid of cable altogether and using another service called Sling TV, which is a streaming service something like ROKU, only one that offers many current cable stations for a $25/mo fee and some other stations (like the ESPN family) for an ala carte fee of maybe $5/mo extra. Right now they don't offer SNY so I wouldn't be able to watch UConn games live but the trend is moving toward cable stations offering a streaming alternative. As soon as SNY offers itself as a streaming station, even for a nominal fee, I will be saying good bye to cable and 200 channels of sales pitches, reality nonsense and endless reruns of old network shows.
Just a suggetion but when I didn't have access to UConn games I would go to a sports bar and ask for the game to be put on where is was sitting.
The only downside was that was forced to drink a few beers.