There are many free SVN hosting services available. I cannot point you to a question here, because as a broad, general question this is off-topic. However, you can easily find many services using your favorite search engine.
However, how fast they are will also depend on your 'net connection, and your location, so your best bet is probably to try them and see which is faster.
That said, you should be aware that SVN is generally a bit slow, particularly over the internet, so you'll probably never get near-instantaneous responses.
If that bothers you, I'd recommend you use a local repository, and a distributed version control system. Most DVCs have SVN integration. Git in particular integrates quite nicely with SVN; you could use a local git repo, and commit to Google code whenever you feel like it. That way, you could even let the commit to Google run in the background, and continue working.
Of course you could also go all the way and use a a DVCs hosting provider, such as github.
Note: There used to be questions about this on SO, like:
However, they have been closed and are only visible to high-reputation users.