You don't have to go far from the Rival Hotel to find a good vantage point to see the city. The hotel's neighborhood is on a slight rise that dominates the island of Södermalm so there are several viewpoints close by. Directly across the street (Hornsgatan) from the hotel you'll see gentle stairs leading up to a small, quaint neighborhood of cobblestone streets. At the end of the the lane you have Monteliusvägen which is a 500 meter long walking path that gives you great views of the Old Town, City Hall and Lake Mälaren. All pictures here are from Monteliusvägen.
Looking back towards the hotel
A little further away, about a 10 minute walk, you have popular Mosebacke Square which connects to Katarinahissen and there you have a view over both Lake Mälaren and the waterfront. Here you will also find the very popular restaurant Gondolen. The popularity is mainly due to the views... be aware that you should book a table here at least 2 weeks in advance. They also have a very nice bar where you can have a drink and admire the views without having to book a table.
If views are your thing, then here are several other spots in Stockholm with great views: restaurant Och Himlen Därtill on top of the Skrapan "skyscraper", historical street Fjällgatan, the TV tower Kaknästornet with restaurant and bar and the newly built SkyView. This last one is a glass gondola that takes you to the top of the Globen Arena, which is located in the southern part of Stockholm. Someday soon I'll try the SkyView and come back with a report...