Pick based on the hotel you prefer. If your interests lie in Roppongi, while Shibuya is closer, there is a direct subway link on the Oedo line from Shinjuku station which gets to Roppongi in 9 minutes. Between Shibuya and Roppongi, there is no direct subway or train service but there is regular bus service that should be around 9-10 minutes as well.
Connecting Shinjuku and Shibuya, the Yamanote line takes 7 minutes.
If you can afford NOT to be in the Tokyu Inn, I'd suggest picking somewhere else. The chain is OK at the budget level but has unfriendly management policies that you might encounter.
Incidentally, the distinction between bars, lounges, and clubs in Tokyo is pretty blurry.