There are a few high-end hotels in Havana with very limited capacity, but the short answer is that state-run mid-tier hotels are a decidedly mixed bag, and there has been no need to meet the demands of higher volumes of U.S. travelers until now. For a list of nice properties that have received good reviews from travelers, please review CheapAir.com’s list of recommended hotels in Cuba.
The other accommodation option for travelers is to take advantage of family-run guesthouses called casas particulares. These ‘private’ businesses have long been an unofficial side gig for Cuban families for years, but the internal relaxation of restrictions for Cuban income have dovetailed with the U.S. embargo relaxation and now creates a more competitive market. That translates to more options and better accommodation for foreign travelers. Especially in Havana, there are many colonial-era guesthouses on offer (some which are quite stately). If you think along the lines of a stateside bed & breakfast you’ll not be far off. Some of these casas particulares you can search and find online.