Well you do know what you want, investing in website. There are several ways to 'invest' in website:
1. Create your own website, outsourse the content and design. But make sure it's high quality.
2. Buy established website(s), don't buy it from Flippa though, lots of trash there you might bought the wrong website. For $10,000 you can get website with $500-$1000 monthly income, or even more than that, depends on monetizing method
3. Launch a tech startup. $10,000 is enough to build an MVP. If you have good idea for a startup, definitely go for one. If you want to know more about this I suggest you to read a book named Lean Startup.
4. Create a web app. The process would be similar to building startups, but it's not particularly a startup. You said that you've learned quite a bit about IM, there's a lot of IM web app so you might be able to 'copy' or create a similar one and make it better.
Any other vertical other than IM may apply for number 4 as long as you (or your partner) have good knowledge
Number 2 seems easy, but trust me if you 'only' got $10,000 don't spend it all on 1 website. But again, you will only get relatively small amount of monthly income if you bought established website. Therefore, I would prefer create one myself.
With $10k investment, don't build low quality websites. You'll only waste your money by doing that