How expensive are 3-star hotels in Dubai,UAE? And are they generally nice and clean? Do American citizens need a visa for a 2-night stay in Dubai?
I'll answer the latter part of the question first, no you won't need a visa. US citizens are entitled to a visa-free entry to Dubai i.e. UAE. Just show your passport to the immigration officer and he will stamp it with a tourist visa valid for 30 days.
US citizens with a US passport that is valid for more than six months do not need to obtain a visa prior to entry to the UAE if the duration of their visit will be less than one month. This includes US citizens with visas or entry stamps from other countries in their passports.
About the hotels, yes they are generally clean and the cost really depends on the season you are traveling and the location of the hotel but roughly it will vary between USD 50-200 per night. You can have a better price idea and booking experience if you use trivago or expedia
Dubai is a fairly clean and modern city, so 3-star is pretty much the lowest you an find and there are really plenty of them. Prices start at around $50 USD per night but I have paid less and a little more.
The hotels themselves are usually pretty well-maintained and clean. Personally I have found service to be slower than elsewhere but really never had anything to complain about hotels themselves.
As @Newton already answered, you do not need a visa for a stay under one month.