You find yourself in Aalborg on Aug 9th. You have 3 weeks. You've never been to Denmark or any of its neighbors before. You are a slow traveler, meaning easily enjoy twice as many days in a town as most travelers. You are over 50, but don't feel it. You love photography even though you aren't that good at it. You can talk to anyone anywhere and you love those opportunities. You love BnBs, good food, great prices. What would you do with your time? Thank you!
Aside from a few days in Copenhagen back in 1972 (I don't feel my age, either), I haven't been to Denmark. I planned to include it in my 2020 trip that didn't happen, but that's no basis for advising you. However, I encourage you to do what I did: Read back through earlier posts in this (Denmark) forum. I found lots of good ideas to supplement guidebook information.
Ribe and Roskilde were my favorite towns. You could easily spend 2-3 days of photography in each instead of a quick RS afternoon. Train travel is a great way to get around Denmark.
Any particular kind of photography you like? While I have to say that three weeks in Aalborg is a bit odd, it is certainly not a bad idea. Any reason for the stay? Denmark often just gets reduced to Copenhagen (and on this forum, Ærø as well) but there is much to see in other parts, and especially Jutland is underrated. My experience with Aalborg is a bit limited but it is a nice town and there are things to see and do there. But if you love photography you should take a day trip to Skagen, or even better, stay overnight to experience the famous Skagen light. Fredrikshavn and Randers are other good day trips. Or Århus if you are looking for a slightly bigger city. From Fredrikshavn you can also take the ferry to Gothenburg if you want an even bigger city and to see a bit of Sweden. It's not day trip distance though, but could be a weekend trip.
But there is more to see than towns and cities, there is a bit of nature to see as well. There are endless beaches on both the eastern and western side of Jutland. Not far from Skagen the 2 km² sand dune Råbjerg Mile and the sand-covered church also popular attractions.
The beaches on the North Sea side are great, though full of German tourists. You can rent a little house on the beach in a place like Hvide Sande.
The castle Kronborg at Helsingor is the basis of Hamlet's Elsinor, and we were lucky enough that when we went, an improv troupe was performing slightly improvised scenes from the play throughout, complete with a sword fight. It was magical! The town itself is also wonderful, with a great history, especially its WWII history. It's an easy ferry ride to Helsingborg in Sweden, too.
Others have already mentioned some great ideas as well, and I would stick with those recommendations.
It's a beautiful part of the world with its own charms, though most of the places where I have spent time aren't generally appealing to foreigners making the most of a trip to Europe.
Denmark is expensive. So is Sweden. That's just a reality. You might be able to get around it a bit, but accept that these are expensive countries.
You could also go down to places like Glücksburg or Lübeck or even Hamburg in Germany. Lots to see and do in Northern Germany as well, and a bit cheaper than Denmark.