7 nights in Croatia. How many nights in each city?

I think there are more attractions closer to Split, so I would base more nights there and less in Dubrovnik (unless you plan on going to Montanegro one day or doing some other day trip close by). Dubrovnik itself is very compact and I wouldn't say that the beach there is the major draw (check out photos of Bol beach on Brac island as a comparison). Two full days there is plenty of time. From Split, you can go to Hvar, Korcula (highly recommended), Brac islands and maybe Mjlet as well (although Mljet seems closer to Dubrovnik). Trogir next door would be a nice side trip as well. Since you only have 7 nights, I would maybe pick 2 bases (3 if necessary if you're staying overnight on one island). Hvar will have the nightlife you're looking for. Make a list of the islands you want to see as a side trip and see if it's better to use Split or Dubrovnik as a jumping point and allocate accordingly (I went in September so that answer differed by season due to ferry schedules).

If you make two day trips, 4 days is right for Dubrovnik. If you only make one day trip, three days will suffice. You may want to consider a day trip to Montenegro from Dubrovnik. Kotor is a neat town to explore and near Budva are some decent beaches. I wasn't that impressed with the mainland beaches in Croatia. The better beaches of Croatia are on the islands. Based on your interests, you may want to spend a couple days on one of the islands and take a day from Dubrovnik or Split to do so. Whether your plan is too ambitious is dependent on when your flights arrive and depart.

Also keep in mind for you planning that the high speed catamaran connecting Dubrovnik to the islands to Split runs northward in the evenings.