Trying to decide where to spend extra day. We will be in Uppsala to start, then to Stockholm and then to VISBY. I have one day leeway to figure out. We do love cities but Gotland seems so intriguing and unique. So: 3 or 4 days in Stockholm ? 3 or 4 days in Gotland before heading to Copenhagen?
I loved my 3 night stay in Stockholm, and I haven't been to Gotland. But while Stockholm is lovely and interesting, it's not like London or Berlin - megacities with weeks of top tier sights. If you have to cut a day from it, I think that will work.
Take a look at Rick's list of Stockholm sights (in his book, or go here and click At A Glance): https://www.ricksteves.com/europe/sweden/stockholm. Then, look at the Tripadvisor list: https://www.tripadvisor.com/Attractions-g189852-Activities-Stockholm.html. The Tripadvisor lists are often odd, since they're user-generated rather than curated, but precisely for this reason, they can turn up things missing from or under-estimated in standard guidebooks.
Estimate how long it will take you to get through your personal Stockholm must-sees. Then, repeat the process for Gotland, understanding it's less about the "sights" than a city would be, and more about the experience (I learned this the hard way on my most recent trip to the Basque country).
Will you have a car for Gotland? If you will, then I think this is more of a personal preference (relaxing on the island or spending time in the city). If you won't, then I would definitely choose Stockholm. Also, what time of year are you visiting? If it were me, I'd add the time to Stockholm.
I spent two full days on Gotland and enjoyed my time there. Visby is fairly small so I spent the first day exploring the town and wandering through some of the ruins. On the second day, I rented a bike and rode out to Tofta Strand (about 20 km outside of town) and spent a couple hours at the beach. I was there in late August which was outside of peak tourist season. To really explore the island, I would have needed a car so a couple days was enough time.
I am not the outdoorsy type, so I can't argue for or against Gotland. I'll just mention that I wanted to see Goteborg, both for its orchestra and for Liseberg [amusement] Park. The latter is much more like Cedar Point than like Disneyland, and has an interesting "local family outing" vibe that should appeal to Rick Steves readers. Goteborg is very urban, however. We were headed to Copenhagen, so it worked well for our trip.