As far as tax implications are concerned, you will be responsible for local property taxes on the property, but other than that, not too much else. The usual caveats apply - make sure the property is zoned for the use you want to put it to and that all the appropriate utility connections are available. Depending on where the property is located, you may be held responsible for making sure the property is kept mowed or otherwise tended in your absence. (Some towns have laws against allowing "noxious weeds" to proliferate if they might spread to the lawns in the neighborhood.)

And, some banks or other financing sources will limit the term of any loans they are willing to make on the property to the duration of your visa to remain in the US.
Cheers,
Bev