Stop 1: Frankfurt, Germany.
Compared to other German cities I've visited, I found Frankfurt to be dirty and unappealing. It was convenient and cheap for flying open jaw, though, and the Sachsenhausen neighborhood was lovely. I visited an applewine bar and had a jug of Speierling and a traditional German meal, all of which was very tasty. The apricot Berliner I bought in the altstadt was also delicious. I was there for four days, but I don't think I'd spend more than 24 hours there unless you have a reason to be there longer. At least it was easy to get around. I stayed at a hostel near the Hauptbahnhof, and the hostel itself was nice, considering it's technically located in the red light district, and it was during the MusikMesse, so it was a little crowded.
Stop 2: Riga, Latvia
This was technically a long layover on the way to Helsinki; most flights between the two cities stopped in Riga or Copenhagen, and I was able to get a 22 hour layover that would allow me to head into town, do a high speed tour, and keep going the next day. I opted for Riga as it was the "road less traveled," and I didn't regret it. I landed a little after 3pm, hopped on a bus that dropped me off a 5m walk from my hostel in the old town, and I had about two hours to cruise around before it got dark. It was snowing pretty hard upon my arrival, but neither the snow nor the cold were so bad that they bothered me. The old town in Riga is full of twisting and curved streets, and I found it hard to navigate, but the locals were friendly; standing around with a map looking lost was enough for someone to stop and offer help. I ate at a restaurant called Ala, recommended by my hostel - traditional Latvian food. Very tasty. The hostel was nice as well; being that it was mid-week and I was only there one night, it was very quiet and very warm.
Stop 3: Helsinki
I stayed with friends the whole second half of my trip. In Finland, I was in a suburb 30m NE of the city, so I actually did not see a great deal of Helsinki proper. It's a very small city, although it looks bigger at first, because all of the buildings are so tall. It is, of course, expensive for eating and drinking, but the various bars and restaurants I visited were all good. It's windy there, but not as crazy windy as Stockholm.
Stop 4: Tallinn, Estonia
This was a day trip from Helsinki while my hosts were at work. I took the 2 hour ferry there and back, which was only 22 Euros round trip. The old town here requires stronger legs than most; not only is it full of uneven cobblestones, it's mostly uphill, especially going up to Toompea. I think I'd say that Riga has prettier architecture, but Tallinn has prettier scenery; I liked them both about equally. I ate at a cafe, and the staff was not particularly attentive, but the food was good.
Stop 5: Sweden
5a: I landed at 9am and had to catch a 3pm train north, so I took the bus into the city. Since I only had a few hours, I went to the Gamla Stan. It was SO windy. It was 12C when I got there, much warmer than the long-term forecast indicated, and bright and sunny, but the wind took the temperatures right back down to BRRR, especially going across bridges and anywhere near water. I didn't do or see anything here that isn't covered already; it was worth the stop.
5b: Söderhamn is a lovely small town two hours north of Stockholm, but if you don't have friends to visit, there's really no reason to go here. Same with Gävle; there's some pretty architecture within walking distance of the train station, but no need to stay.
5c: Uppsala was a quick tour by car, as I was staying with a friend several miles outside the city. The old town is pretty standard, and Sweden is holy crap expensive for eating and staying, but the countryside here was so beautiful; full of rolling farmlands and groves of trees. It turns mostly to forest another 40-60m north of the city, which is also gorgeous.
And then it was back to Arlanda and on home...