Boogar,
Here's a list of USA-TT Events:
http://www.teamusa.org/usa-table-tennis/events As pgpg wrote, you pay a $20 tournament fee (@ tournament) and fees per entry (each entry could cost $15-$50). Most will be held on Saturday's or Sunday (some on both). That will leave you Monday-Friday open.
The US is huge and not like going from Berlin to Hamburg. You need to tell us the city (airport) you arrive and city (airport) you depart. That would make it easier.
I am assuming you will land in New York(?) the US East Coast. Here is a sample of events you could visit:
Date - Club - City, State
July 02, 2016 - HCTT Circuit 2016 - Columbia, Maryland
http://www.teamusa.org/USA-Table-Tennis/Events/2016/July/02/HCTT-Circuit-2016
July 16 - 17, 2016 - LYTTC July Open - Dunellen, New Jersey
http://www.teamusa.org/USA-Table-Tennis/Events/2016/July/16/LYTTC-July-Open
July 24, 2016 - NYISC July 2016 Open - College Point, New York
http://www.teamusa.org/USA-Table-Tennis/Events/2016/July/24/NYISC-July-2016-Open
I chose the US East Coast as it's the densest population with TT (drivable distances)
If you have spare $$, and if you are lucky with an open slot, you could fly out to the US Nationals. Many days of TT. You will need to fly out there (6+ hour flight from NYC)
http://www.teamusa.org/USA-Table-Tennis/Events/2016/July/04/2016-US-National-Championships
Now, there are clubs on the East Coast too that you could visit Monday-Friday.
Let us know more airport details, we could build a better itinerary.
PM me if you have further questions.
Chuck