Tallin has some guys who do cycle taxis and when we went there were taxis at the top of town as well as at the bottom and plenty of bars and ledges. Our guy did Tourism management at Preston in England! We were there on a Saturday and there was a market in the town square. Old town is a beautiful medieval town, occasionally feels as if you are in a theme park- there are some genuinely talented craftspeople in Estonia and an opportunity to buy their work is definitely there at the market and in the many many shops.
In Copenhagen we concentrated on the Museum of Design and saw some really unique beautiful things, again concentrating on maximum things to see per pace walked.
If you want to see the Viking exhibition for certain at the national musuem it may be advisable to book in advance. Tivoli opens at 10 am. Queues for boat rides can get quite long in summer so if this is on your agenda you may want to go early although they were not available as soon as our transfer landed.
Beautiful town, great atmosphere market has loads of wares from talented local craftspeople. People on walking tours looked bored in comparison to people just doing their own thing and hopping on and off standard public transport but look at others descriptions of their experiences of these tours as I may have misinterpreted!