At the places listed below, you can get free feedback about your website/app design and usability (UX), and sometimes about the underlying business idea. I think this is the most comprehensive list you can find — and if something is missing, pleas post a comment and tell me.

Usability Testing Exchange

That's this website. Go to the homepage. You'll get back as much feedback as you give to others, counted in characters ( & Math.log).

Reddit

Reddit is a place where about 30 million people meet online and talk about different things. At Reddit, there are sub-communities, called "subreddits", some of them about design and UX feedback:

• /r/design_critiques — Post a topic and get feedback about your design.
• r/web_design/ — You can ask for feedback in the Feedback Friday weekly topic.
• /r/SideProject — Feedback about your design, UX and overall idea.
• /r/AlphaandBetausers — Find people to test your web app. My impression is that 99999 people posts apps to be tested, but essentially no one has time to tests someone else's app. So I'd be surprised if you get any help from here.
• /r/Startups — Feedback about your underlying idea, + perhaps also a bit about the design, if you post in the "Weekly Feedback and Support Thread" (example). There're also monthly share-your-startup threads, example.
• r/growmybusiness/ — Apparently similar to /r/Startups above.
• /r/RoastMyStartup — Feedback about your underlying idea. The people here, in RoastMyStartup, might have a bit negative pessimistic way of writing, in my experience.
• /r/Entrepreneur

Hacker News and Designer News

• Show HN (Hacker News) — if you've made something other people can play with and try out. The people at Hacker News can give you feedback and ask questions. Read the guidelines and instructions.

• Show DN (Designer News) — I think this is like Show HN, but needn't be something people can play with and try out. Instead, they're interested in a cool / beautiful design. Read the guidelines.

Other web design places

• https://www.sitepoint.com/community/tags/site-review — I got helpful feedback about Usability Testing Exchange here.
• https://www.warriorforum.com/website-design — this is a business & marketing forum, and design is important for marketing, so they have this category dedicated for website design feedback.

Forums about marketing & business

Your title and tagline matters. You can go to a forum about business and marketing, and describe your business idea, and post your title & tagline, and ask for feedback. While you're there, help someone else too, in exchange :- )

• https://www.warriorforum.com/copywriting/
• https://www.marketingprofs.com/ea/ — there're many sections: taglines/names, website critique, copywriting.
• /r/AskMarketing/ (Reddit again)

Usability testing websites

Search the web for "Usability testing". You'll find lots of stuff, but everything is expensive (I think) — except for one:

• https://userbob.com/, it's not free, but inexpensive (as of September 2017). I've used it, and it worked fine for me.

Freelancer portals

You can sign up at e.g. Upwork, and pay for someone to review your website for about an hour. Not free, but can be inexpensive. The freelancers might not want to tell you, though, if they think the whole thing you're doing is pointless.

Feedback exchange websites

There are ... were ... exchange-feedback / peer-review places, fairly similar to Usability Testing Exchange. All of them are gone now? People in general didn't seriously try to help each other. Instead, they posted spam, or copy-pasted the same useless one-line-feedback to everyone. Or sometimes they submitted their site, just to get a rel=follow backlink. Here're the alternatives I've found:

• http://www.criticue.com/ — I've gotten some useful feedback here, but often people seem to post the same generic one-liner to everyone. Seems it's gone now, has been offline for fairly long.

• http://feedbackroulette.com/ — has been shut down. One was supposed to get more feedback, if one gave more feedback. Didn't seem to work well to me, though — for example, I got back useless one-liner after having spent 15 minutes reviewing for someone else and written a few paragraphs.

• http://www.conceptfeedback.com/ — has been shut down. People didn't help each other. Many posted spam.

• http://feedbackexchange.org/ — despite the name, doesn't work as a feedback exchange (as far as I can tell). Instead, people ask for help, without helping others back. The website staff sometimes reviews and give feedback though. — Seems it's gone now.

You have more suggestions? Or corrections? Feel free to add a comment below.