Stockholm

Hotels:
Hotel Elite, Birger Jarlsgatan, Stureplan. Great value 3-4 star hotel, right next to all the bars & nightclubs in Stureplan.
Restaurants:
Grill, Drottninggaten 89. Great fajitas & grilled food & atmosphere. Trendy bar/restaurant.
Kungsholmen, located in Kungsholmen. Great sushi, variety of foods, and its own ice cream bar! Trendy bar/restaurant scene.
Nightlife:
F12 Terrassen, Fredsgatan 12. Awesome summer outdoor nightclub, located on a staircase.
White Room: Jakobsbergsgatan, Good club, more of a NY-type scene, and naturally- all white.
Plaza Club, Spy Bar, Solidaritet, Sturecompaniet, Bistro Jarl, East, Café Opera. Other bars & clubs, scene varies depending on the night and time of year.

Copenhagen

Restaurants:
Cafe Victor is always a favourite for good brunch, and a decent evening bar scene (plenty of other good bars on same street- Ostergade), http://www.cafevictor.dk.
Zeleste is a lovely tucked-away seafood and steak restaurant near Nyhavn on St. Strandstrasse that resembles a farmhouse.