Try Tom Bowers
http://www.subguns.com/
or Sturmgewehr
http://www.sturmgewehr.com
A transferable pre-WWII 1920's Thompson will cost about $20,000. A transferable WWII M1A1 Thompson will cost about $12,000.
You need to be 21 years old, no felony convictions, pass a FBI background check, get a LEO signature, and pay a $200 transfer tax to the BATF. Count on the above taking about a year.
The seller of the Thompson will probably want the money up front, so you will be out the $20k for awhile before you can shoot it. On the bright side, whatever Thompson you buy will probably appreciate 20% in the year you are waiting for the transfer.