Assuming UK still has Cal and isn't caught doing anything shady they are the likely favorites. Everyone at UK but Wiltijer and maybe Teague is likely gone to the NBA after this year or graduating. They need players and have playing time everywhere available.
I wouldn't count Providence out. They have a very solid (top 10 at least) class next year with Ledo, Dunn and Fortune. Not to mention they have some solid pieces coming back next year. Their backcourt could be very good with Ledo, Dunn, Fortune, Cotton, Coleman and Council at the 1-3. That is deep and talent laden backcourt, on paper. The frontcourt is their big hole, but Henton is a good energy player. Noel coming to Providence would make them a dangerous team (assuming Cooley can actually coach and Ledo qualifies) and hide their other bigs weaknesses.
I would think this minute Cuse is third. I would say a close second to UK if Melo leaves. Cuse's main issue right now is obviously playing time with the bevy of experienced post players Melo/Keita/Christmas/Southerland and DC coming in.
UConn is probably fourth in the running for Noel, right now and a distant fourth at that. Even if (and purely theoretical here) Noel liked UConn #1 and wanted to go to UConn it would be difficult and would depend on 3 things: scholarships, who goes pro (considering how this year is progressing, no UConn player is guaranteed to leave) and NCAAT eligibility. UConn as it stands needs either the NCAA to give back a scholarship (one lost to APR, considering the APR the past year and assumed this year UConn can ask for it back based on progress) or have someone leave. If Noel were to come, they would need both APR scholarships back or two people to leave.