For reference, in Seattle proper at your budget, a SFH in a stable, quality elementary school zone without access to private beach and with 15 year waitlist for nearby pools will get you this:
https://www.redfin.com/WA/Seattle/6011-43rd-Ave-NE-98115/home/314102
Redmond and Bellevue are vast but good options. If it weren't for your job in Renton, I would suggest Shoreline or Edmonds. If you can tolerate more traffic, look further into Issaquah and the Klahanie part of Sammamish. Your budget can put you in a nicer SFH in Issaquah Highlands or Klahanie and shave 30 minutes off of your ski commute time:
https://www.redfin.com/WA/Sammamish/24214-SE-40th-St-98029/home/437165
Newport Hills, Newcastle and Somerset are not glamorous but are close to the lake, easy-ish access to the airport, and you might get lucky and find something in your budget in Newport Hills. It's changing fast and feels pretty transient right now with a lot of flips, teardown and rentals:
https://www.redfin.com/WA/Bellevue/12631-SE-68th-Pl-98006/home/415936
Also consider Renton Highlands. You won't be able to access a neighborhood like Maple Hills with your budget, but there are some other good possibilities. Renton will not get you the same quality of middle and high schools. This is what you can afford in Renton:
https://www.redfin.com/WA/Renton/6213-SE-3rd-Pl-98059/home/246693
You'll want to think about the kind of neighborhood you want, the kind of housing compromises you'll make, and what kind of diversity you want/don't want- some neighborhoods are very homogenous like in Northern VA and you can find yourself left out. You also need to be careful about school zoning because Bellevue has some not great elementary and middle schools and some that may close. If you're looking for things like a neighborhood beach club or a swim club, there are some pools without wait lists and others that are 10-20 year lists. Many people drive 15-45 minutes to access a club without a wait list but it's a typical situation so people are welcoming. You are not going to be in a beach club neighborhood, unfortunately, but there are public beaches on Lake Washington and Lake Sammammish State Park is great.
For skiing you will probably go to Snoqualmie Pass if you are in Bellevue, but once you get further south Crystal becomes more possible. It's an hour or less to Snoqualmie Pass unless the weather is terrible. But you need to arrive an hour before lifts run during lesson weeks or you won't have parking. People go to Stevens Pass from the Eastside but it's further north and not worth the effort. Buy your passes now for next year to save money.
If you can describe where you are now (or a similar area), I can try to give you areas that might be a fit. You won't be living on the water, but luckily it's hard to go about your day in this area without having to go near it.