There are no restrictions on foreigners buying US property. However, from a tax point of view there are a number of disadvantages, and these will exist up to and until your become a US citizen. Look up CGT liability and taxation at death on the IRS.gov site. In addition, for some states (Florida, for example) you will pay a heavier burden in property tax as an alien.

Note that buying a property gives you no right to live in the US. If you are of retirement age, you could possibly apply for a B2 visa as a "snowbird" and spend up to 180 days in. However without this, the VWP only offers 90 days. Using these visas, you should spend at least as much time out as you do in, and even then there is no guarantee of entry. It should also be noted that spending 180 or more days in the US will mean that the IRS consider you a resident for tax purposes, even if USCIS do not.

Beyond that, there are various visas which would allow you to spend a longer time here. Generally, they involve $$$.