There are basically no limitations for any foreigner to buy residential real estate in the United States. (Note: there are limitations on the purchase of certain businesses, at least vaguely related to defense of the nation.)
As a Russian, your visas are likely to be very limited on how long you can remain in the United States. You need to make sure to adhere to the conditions of that visa and your I94. (Unless you have a status other than B1/B2 tourist/Business).
Foreigners with no residency regularly purchase real estate in Miami, both as second homes, and for investments.