Alas the Russian Ministry of Foreign Affairs web site does not seem to have its own Travel Advice section for tourists going to the USA, however the UK Foreign Office site does make it sound a bit scary
http://www.fco.gov.uk/en/travelling-.../united-states

As for the sponsor part, you won't really need to worry as it sounds like you will be on a tourist visa and hotels will register you. It would be different if you were working or studying or on a private visit staying with friends/family.