There are a lot of hiking trails here. Anything from a couple hours to backpacking and car camping. I've been to quite a few of them and have tons of recommendations. Here are some good day hikes:
Rattlesnake Ledge - There are no actual rattlesnakes on this one. It's an easy hike that's 4 miles roundtrip with a great view at the top. It's probably the most popular hike in the area. At the bottom is Rattlesnake Lake which is always crowded during the summer since it's a great place to swim and you don't need to buy a pass. We've also been here at night during meteor showers.
Twin Falls - Closed at the moment but it should be open later this year. I think this is less than 4 miles round trip and less elevation gain than Rattlesnake. There's no mountain top but the waterfalls are really nice.
Snoqualmie Falls - This is a very large waterfall that you can practically drive right up to. There is a resort right at the top you can stay in as well. It's a nice stop during the day that doesn't take too much time. And there is Snoqualmie Brewery and an old train yard right down the road.
Little Si - One of my favorites.
If you go car camping, there are more options in the North Cascades. For instance, Yellow Astor Butte, where I took this picture: