Dear acastino,
I had a look at what is available in Rome and the main problem I can see with you wishing to follow a course is your restriction on dates.
http://www.dantealighieri-roma.it/gb/corsilinguaita.htm
has courses but they run from the start to the end of the month. However, this site is a good resource and they may help you find suitable personal tutors. This association has branches all over the world; find the nearest one at:
http://www.ladante.it/lenostresedi/index.asp
[select Stati Uniti if you are in the USA] for future reference.
See also courses for foreigh students at the 3rd univerity in Rome at:
http://www.uku.fi/~postman/kv/kesakurss ... anieri.pdf
this may just fit with your dates in July, but is a bit expensive (800 Euros).
Regarding personal tutors, I have been unable to locate anyone I know in Rome who
provides this service but I note there are several professionals offering this kind of service on:
http://lavoro.trovit.it/lavoro/italiano-per-stranieri
[Look for ITALIANO PER STRANIERI and Roma for location (4th message down)]
and other personal announcements in the following links:
http://roma.bakeca.it/lezioni-traduzion ... rzk2703667
http://www.mercatino-annunci.it/mercati ... io799.html
http://roma.bakeca.it/lezioni-traduzion ... c251140134
http://cultura-italiana.it-schools.com/ ... ndex.shtml
Good luck!
roma55