AREAS OF TOWN:
The most desirable and expensive area of town is Östermalm. From Östermalm, you will be able to walk to almost everything you will want to see and there are loads of cute cafes and restaurants. Many of the main museums and sights are in this area of town. These days, almost the entire main island (which Östermalm is on), including Norrmalm and Vasastan is pretty expensive and chic. The only area to avoid is near the Central Station. The area surrounding there was built up in the 60s and 70s and although very central, is not that charming. Most of my hotel recommendations will be in Östermalm/Norrmalm, mainly because everything you will want to see is here and because I know this area of town the best.
Gamla Stan is the historic old city. This is probably the most touristy area of Stockholm, but is nonetheless still a lived in area and is extremely charming. If you go off the main touristy street, you will find charming cafes, antique stores, and little boutiques.
Södermalm is the "Soho" of Stockholm. It is hipster central and all the coolest hipster restaurants are in this area. Historically, it was where the lower class workers lived but now is almost as expensive as Östermalm. Parts of it are very charming but other parts are a bit blah. I am not in this area of town that much, so I don't know much about the hotels here.
Kungsholmen is another area that you might think of. It is a bit off the main path and doesn't have any museums that I know about,other than of course the very famous city hall, which is well worth a visit. It has many great bathing areas and it is lovely to walk around the entire perimeter of the island, providing you have good weather! It also has tons of cute cafes and restaurants. Make sure you are in the side near to Vasastan/Normalm.
Public transportation between all these areas is extensive and easy. Stockholm is a great walking city and is not that large. I live in the NW part of Vasastan (near St Eriksplan subway) and I can probably walk to most of the museums and areas that I have discussed within 20 to 40 minutes.
The Grand Hotel is arguably the best and most luxurious large hotel in town and it is not a chain. It is one of the most expensive in town so it may be beyond your budget, but you can use it to benchmark prices. The Cadier Bar off the lobby is an amazing place for people watching, as many famous people stay there. The view is gorgeous overlooking the water. Their afternoon tea is the most luxurious in Stockholm. They also have a number of good restaurants, including Mattias Dahlgren's Matbaren, a delicious modern Nordic tapas style restaurant. https://www.grandhotel.se/en
Lydmar is a very chic boutique hotel, next door to the Grand, and possibly even more expensive. A nice place for lunch in the summer is their terrace bar, hidden upstairs and their main restaurant is very chic and popular with well-heeled locals. http://lydmar.com/
Raddisson Blu Strand is in an equally desirable location on the water but about half the price. Normally, I wouldn't recommend a chain hotel like this but the location is so so good. https://www.radissonblu.com/en/strandhotel-stockholm
Story Hotel also has a great central location but is a smaller boutique hotel with a fun bar/restaurant. http://storyhotels.com/riddargatan/
Nobis is also well located on a square off the most expensive shopping area. A bit cheaper than the Grand and Lydmar. The lobby is a nice place for drinks. http://nobishotel.se/en/
Hotel Diplomat is another waterfront hotel with some great bars. I especially like the little wood paneled upstairs bar on the first floor. It is small and intimate and a great place for a conversation. About the same price as Nobis. http://www.diplomathotel.com/en/hotel-diplomat-stockholm/
Hotel Kung Karl is a Best Western I think, although I wouldn't guess that from the lobby which is very chic, with a pretty bar area. It has a great location in the middle of everything and has a really nice weekend brunch with a cute homey atmosphere. Relatively inexpensive for Stockholm. http://www.kungcarl.se/en/
Mornington is another little hotel in Ostermalm. Modern. Across the street is a great restaurant/bar (Nybrogatan 38).
Miss Clara by Nobis is on a busy not so charming street. But it is still very central. Rooms are modern.
Urban Deli Hotel is just down the street from Miss Clara. Urban Deli itself is a hip cafe/restaurant/bar/shop, trying to be Dean and Deluca in NYC, if you have been there. I think the rooms are probably pretty basic.
Haymarket is a new hotel. I have no idea what the rooms are like but the bar/restaurant area is very chic and crowded in the evenings. It is on a market square, so it is quite nice to come out in the morning to the vegetable and flower stands. Nip downstairs on the other side of the square into the food hall to have a bite to eat or just to admire all the lovely food on display.
Freys Hotel is a smaller located in the area near the Central Station that I told you to avoid. But it is on a little side street and I recommend it because I have been there for a seminar and they had amazing service with all sorts of nice details. Assuming that it is the same management, then I am willing to bet that the hotel is very well run. They have a Belgian themed restaurant that is nice.
Lord Nelson/Lady Hamilton are little old fashioned hotels on Gamla Stan. Filled with creaky staircases and doilies. If you like history, then it is full of dusty charm. http://www.thecollectorshotels.se/en/lord-nelson
Rival is in Södermalm. I have been there for their nice breakfast buffet. To be honest, I just looked at the prices and I was a bit shocked at how much it was--I don't think it is worth that much! But if you are longing to stay in Södermalm, then you could consider this. http://www.rival.se/en
Finally, you might try airbnb. It is very popular here.
Do you have a favorite hotel in Stockholm?