Gamla stan(old town), VASA Museum, Royal Palace,
Drottingholm Palace(where royal family actually ives)( get boat there next to City Hall)
City Hall, take a tour
If you want to go out in the islands, take the boat to Fjaderholmama and have have a nice fish lunch by the water.
Millesgarden, sculpture garden at Carl milles' home.
Get a transit pass that covers ferries, buses, and the subway.
For hotels, look at the local chain, Scandic for good deals.

For hotel suggestions you really need to give us a budget - a specific amount in SK - keeping in mind that Sweden may well be the most expensive country in Europe.

Bill...NYtravelers's comment above is right on the money. But I'll recommend lodging at The Mornington Hotel which served our purpose well. It should no more than $150...well- appointed, located in Ostermalm district and walkable distance to Gamla Stan. Excellent buffet breakfasts.

I don't do trip reports, but instead I am attaching some familiarization pics which will give you some feel for the city and what to see.

My guess is that you will like Stockholm and its environs as we do after two visits. There is a popular food hall just a block from the Mornington (which I've pictured) that's handy for lunch or dinner at almost stateside, "reasonable" prices. In Gamla Stan, try "Gasganda" for a salmon salad lunch, or around the corner at "Sally's" for the Sally's Tower mound of shrimp, avocado and succulent mussels. Enjoy your visit. Where else does your cruise stop? If Norway, Denmark and/or Finland, St. Pete, I'll be happy to attach additional "familiarization" pics.
Stu Tower

https://picasaweb.google.com/stuarttower/Stockholm#

Would like to keep the hotel $200 per night or less!

Hi Stu
We are going to visit Copenhagen ,St Petersburg ,Helsinki, Tallian..
Thanks

Stockholm is the capital of the country and quite international. Local lifestyle is, at a glance, as in any other large European metropolitan area. And it has worthwhile tourist attractions.

http://www.flickr.com/photos/mksfca/sets/72157623071349528/show/

You will be in Stockholm for a full week before a cruise? Do look at the Scandic website as they often have incredible offers online and have many properties in a range of prices in the city. Our Swedish friends recommended we check them out which we did. Huge free breakfast, deals like stay three ,one night free, free wifi when we went to Stockholm.

I fear that in Stockholm that budget may get you only a 2* (budget) hotel at that time of year.

Perhaps check the cruise line to see if they have any pre-cruise offers. Or eurocheapo.com. But many listed are hostels, or have shared bath or no windows, etc.

The only (moderate) hotels I know there are asking about $350-400 per night.

You have been given some good places to see in Stockholm.

If you are there for a week you can just about see every tourist site to your liking.

tower and Michael:

Nice pictures!

Bill....scratch the Mornington...checked it out and it's gone from $150-ish to $250-ish in two-and-a-half years. Evidently it has been totally reovated and was bought by a new UK hotel group, hence the increase. I knew it had to be a bargain at $150. Anyhow, here's the web: (No doubt, these days anything under $200 will be difficult to find)

http://www.mornington.se/stockholm.aspx?lang=2&pageId=1

Found a few nice hotels for around the $200 range.. What is the best way to get to the hotel downtown from the airport?

Gamla stan and drottingholm are two recommendations I would ahve as well. It has been 8 years since I have been back to Stockholm, but those are must see's while there. If you can there is a city just north called Linkopping that has a huge zoo/park. The have a dolphin shoe, a tram ride through the park, beautiful water way to explore and a wildlife safari drive through. Interesting and a fun way to spend the day.

Good luck find a hotel for less than $200/night in Stockholm centre the first week of June 2013! The youngest daughter of the King of Sweden is getting married on June 8th and there will be days of celebrations!

I loved the Archipielago!

There is a wonderful train, Arlanda Express I think, from the airport to Stockholm. You can get a senior discount if that applies.

If you travel into town on the Arlanda Express, it will deposit you about thirty yards from the entrance to the Nordic Sea Hotel. Of course it does have the trendy and touristy Ice Bar, but that's not a bad thing. You are in a good location, a few minutes from Sergels Torg, which is in the midst of Stockholm's commercial district and is a good place to get the pulse of the downtown. Gamla Stan isn't far, but be sure to get off on the back streets when you visit. You have a reasonable chance of fine weather in early June, and wandering on Djurgarden, one of Stockholm's many islands, is a worthwhile way to spend a day. Rosendal's Tradgard is a lovely biodynamic garden near the Rosendal Castle on Djurgarden. They have an exquisite bakery and a lunch spot that draws all manner of families and strollers (and in the two times I've been there, no tourists except for me and my wife) on a sunny day. It seems as if they have many regular customers, but they're very friendly to newcomers (and just about everyone can easily switch into English in Stockholm). The Fotographiska (photography museum), a short walk across the water from Gamla Stan is one of Stockholm's newest museums, and the view from the upstairs lounge across to Skeppsholmen is worth a visit. On a sunny afternoon, the light is exquisite...and so are the photographs in the museum. Speaking of Skeppsholmen, that island is also worth a visit, primarily because of the Moderna Museet (modern art museum). If you venture out onto the archipelago, and I'd certainly recommend that, taking a ride out to Sandhamn, which is viewed as the farthest point in the local archipelago is great fun because you get to see the changing architectural styles of all the houses built along the archipelago over the years. Try to take the smaller boat (Strömma canal boat) that goes through the narrowest channels. It's a slower ride (about three hours) than the big boat, but you'll see more and have about two hours on Sandhamn between the outbound and the inbound. We haven't made reservations in advance so we could be sure of a nice day, but we've tried to be at the dock about 45 minutes before sailing to be assured of getting on the boat. Another interesting archipelago adventure is Vaxholm, with its fortress that was used as defense from the 16th to the 20th century. An another vote for Millesgarden, which is a most enjoyable way to spend an afternoon. Stockholm is my favorite city, and I could rattle on about places my wife and I have enjoyed, but you have a lot to start with from what I've read in this post. A great spot for grabbing a beer in the afternoon is Flyt, a bar on a boat that looks across from Gamla Stan to Slussen. Also a prime spot to get the vibe of the city. And we haven't even spoken of Sodermalm! Stockholm is my favorite city, and I could prattle on with many more suggestions, but some have already been made here, and you can have a very full week with what is suggested here. Hope you don't have trouble getting a room because of the wedding. E-mail me if you have more questions.

chriskil wrote: If you can there is a city just north called Linkopping that has a huge zoo/park. The have a dolphin shoe, a tram ride through the park, beautiful water way to explore and a wildlife safari drive through. Interesting and a fun way to spend the day.

Does anyone know where this zoo park is, since it is not likely to be in Linköping (which is west of Stockholm and about 2.5 hrs by train?)

The zoo park is in Norrköping, which is about 2/3 of the way between Stockholm and Linköping. That's almost a two hour trip from Stockholm. If you decide to visit Kalmar and the Glass Kingdom, it's not a bad place to stop en route (the Glass Kingdom is about 4 hours from Stockholm), but it is a long day trip from Stockholm. Uppsala (with Linnaeus's garden and a number of places worth seeing that are associated with the University of Uppsala) is a bit closer as a side trip (an hour or so) as are Drottingholm Palace and Gripsholm Castle at Mariefred, both of which can be reached from Stockholm by ferry.