"Nice website" - I hear that often. Then I open the page and it takes seven seconds to load, text overlaps a button on mobile, and I don't know where to click to send an inquiry.

Beauty is part of the equation. But a good website isn't always the flashiest one.
Test 1: Do you know what the company does in 5 seconds?
Open the homepage. Look for five seconds. If you can't say "this company does X for Y people" - the site isn't doing its job.
Test 2: Mobile version (not optional)
Over 60% of traffic on sites I build comes from phones. If someone praises a site but hasn't opened it on mobile - that opinion doesn't count much.
Test 3: Speed
Open the site and feel if you're waiting. If you feel nervous after three seconds - users feel the same, they just leave.
Test 4: Does it lead to action?
Every page should answer: what should the user do next?

Test 5: Trust
People buy from people and companies they trust. Real photos, references, contact details, HTTPS.
Test 6: Content that helps, not just sells
A good site answers questions clients have before they call.
What is NOT as important as you think
- Animations on every element
- Latest design trends
- 50 pages when you need 5
- "It must look like site X"
Good website vs good web project
Sometimes a client doesn't need a website - they need a web app, internal system, or automation. A good developer will tell you that.
A good web project solves a concrete problem. If after three months the site hasn't changed anything in the business - either the site isn't good, or nobody's tracking results.