Interesting. Now I'm curious. How many people (here) have built an MVP without having a business model?
As far as promotion, I'd hit every social network (and run some ads, Twitter can be very cheap to run ads. I have created a blog post about running ads on the cheap on Twitter with high engagement).
I'd also try to get your site listed on beta list and feed my app and earlibird and product hunt and...the million other sites/directories out there.
Post on Hacker News (repeat posts when you have some insightful blog posts).
Ensure you do have a blog. Getting mindshare is important and it provides you with fresh content to link. Otherwise you'll come off like you're spamming everyone on all these outlets.
It takes a good bit of time to do all this. Manual labor unfortunately. You can automate some of it, though I always caution people about buying followers and automating things. Again, you have to watch out for coming across as being a spammer.
I'm always free and happy to discuss strategies and bounce ideas around!
And congrats on getting your MVP done! That's no easy feat.