I wish to find some hosting for any small Ruby (Sinatra) application that utilizes Graphviz and Us dot.

Heroku is generally my personal favorite since it is a) Free, b) Simple, and c) Scalable. Heroku does not do Graphviz and Us dot, so I am searching for an alternate. Any ideas?

I have been happy with bluehost.com. They support ruby/rails, etc. even though they don't provide graphviz or us dot 'out-of-the-box,' they offer spend accounts. I have labored with Graphviz and us dot before on the different, but similar, system before. If you are prepared to have a crack in internet marketing from the party prompt, bluehost could be more that acceptable.

They likewise have fantastic customer care. (With no, I am not associated with them whatsoever. Only a customer.)

Dreamhost appears to let you install Graphviz:

http://wiki.dreamhost.com/Graphviz

Hope this can help you.

If you are willing to handle a removed lower 'Viz api, Google Charts API now supports GraphViz experimentally.

I'd suggest moving to some VPS. I personally use Slicehost, and they've plans beginning at $20 per month.