Wonderful city to travel solo in, so much to do!
Traveled solo through the city but was never bored. Beautiful streets, Tivoli Gardens is well worth the cost to get in, beautiful place to have lunch or dinner at any number of restaurants, or take a picnic to have on the grass and the rides are really good, although make sure you buy a multi-ride pass (paid for itself after 3 roller coaster rides!). The zoo is great (and huge!) and the Aquarium is wonderful (although a bit smaller that I was expecting).
Insider Tip:Buy a transport pass from the ticket office (get there early, if you arrive after 10:30am expect to wait in line for at least half an hour) at the central station (24, 48 or 72 hour passes), makes getting around super easy (can be used on all buses and the metro as well).