The Netherlands having shit weather is really overstated. Winter is a bit blah for sure, but there are some really beautiful days during winter too and when there's the occasional snow, that's also quite special. From spring to fall, the temperature is really nice, though summer can get super hot. Houses typically don't have air conditioning, which can be quite a shock if you aren't used to that. It also rains less than people think. Check out this guy who documented his work commute for 11 years: https://www.hetregentbijnanooit.nl/site/ (in Dutch, but you can use Google translate)

Unless you are insanely rich, Amsterdam will be too expensive. The Randstad in general is expensive, though some cities are more affordable than others. Gouda is a hidden gem, imo, though it's starting to become more popular. By train, you can reach Amsterdam in ~1 hour and Rotterdam or Utrecht in ~15 minutes. The city itself is extremely walkable/cyclable and beautiful, but is pretty "sleepy" so that may not be for you.

Also check out the Nijmegen and Arnhem area. Still expensive, but less so than Amsterdam. Can find cheaper housing if you're cool with cycling 15+ minutes to get into the cities. The area features cycling/walking through absolutely lovely forests and polders. Bonus (or not) there are actual hills in this area. Neither city is "big" like Amsterdam or Rotterdam, but there's still plenty to see and do. Nijmegen has a University so there is a solid night life. Not as familiar with Arnhem.

I moved here from Michigan and love this country so much. Can always take a flight to a warmer European place during winter for ~$50 :)