You need a visa to visit Harbin, but do not need a sponsor, and you can join a tour, I think.

For most nationals, that includes americans, you need visa to enter China. Thereafter, most places are free to travel. Your best entry point would be Beijing or Shanghai. There are plenty of flights from these 2 cities. Domestic flights to Harbin via these 2 cities are plentiful. No tour needed at all. Your consideration should be fares to Beijing or Shanghai in terms of cost & whether you plan to visit cities around these cities. My preference is for Shanghai as there are more places to go around. Of course, if it's your first visit, Beijing is a must. However, winter time is not so good for Beijing as most sites are outdoor & it's truly freezing cold! As soon as you get to Harbin, just get to your hotel & the concierge will be able to take care of whatever arrangements you need. No hassle at all! Joining a tour will involve too much unnecessary expenses. Not worth it at all.

No need for a sponsor. Just book a hotel reservation b4 you apply for your chinese visa.