Just back last night from our first visit to Stockholm. This may help -
We arrived at Arlanda airport and had pre-booked the Arlanda Express tickets. It is more expensive but 20 mins to centre. We stayed at the Radisson Blu Waterfront which is right beside the station. There is also another one Radisson Blu Viking also close by and we got confused when we arrived. On our departure there was a sign in the hotel which said next Arlanda Express 6 minutes - we made it so you can see how close we were.
We don't normally go for hotels close to the station as in a lot of places we have found these areas a bit more run down however there were no issues in Stockholm. There was no noise in the hotel whatsoever but ask for a waterfront room as the others look onto an office block. We were celebrating our wedding anniversary and they had booked us into a waterfront room.
We bought a 72 hour travel card and this was great for all trams, metros, buses although we also did a lot of walking.
Weather varied between cold and very cold!!! but we expected that and the sun shone. It did snow a little which was lovely. There was snow on the surrounding ground but most of the pavements were clear.
Took the guided tour at Nobel Museum - a lovely museum. Also visited Nordiska Museum and the City Hall among others.
It was far more expensive than UK for eating and drinking but there are lots of lovely restaurants etc. and we expected it to be more expensive. My motto is - you are there to enjoy yourself so you have to pay the higher prices and I do like my glass of wine and nice food. We didn't have breakfast in the hotel, just went out for coffee and croissants etc.
The people in Stockholm are friendly and at no time did we ever feel unsafe.
Thanks for all the helpful comments on the forum.