I have always wanted to do a coastal hike, but never got to... If you can do that, do that.
Regarding Mount Rainier NP:
If you're going to break things up into several hikes a fun one is hitting all seven peaks on the Tatoosh Range, south of Paradise. This can be done in one day, supposedly, but I never succeeded in doing so. (Though this was before I went UL.) You definitely get views, and I saw mountain goats there several times. It could easily be an over-nighter though it is within MORA so you'd need a backcountry permit, but they aren't hard to get since they reserve a lot for walk-ins. The route is in the "75 Scrambles in Washington" book, which is in general good resource for routes that lack hordes of amateurs to harsh your zen thing. You leave your car in Longmire and hitch to Paradise to start the hike. Thus it isn't a true loop, but it's close. Also, there isn't really a trail for most of it, per se. You follow Marmot trails. Thus I've never seen crowds except on the trail up to Pinnacle Peak at the start and on the Longmire Trail at the end. But if you're not up for routefinding you might not want this one.
In general though I like Sunrise more than Paradise. You start higher, and the crowds aren't as ridiculous, and the views are awesomer. It's just a hair harder to get to. You could easily make a loop out of the trail system around there, perhaps with little out-and-backs jutting from the loop. There are many options- just get a MORA map and pick a route. (Though many of the Sunrise trails are on GoogleMaps terrain view if you zoom in enough, if you want to make a quick check.) Anything around Sunrise will have wicked views. Starting at the Sunrise lot and making a loop down along White River and then back up comes to mind, but it is vigorous. Making a day trip of hiking out and back the Burroughs Mountain trail gives particularly stunning views, but hike ALL the way out- most tourists stop at First Burroughs, but there is actually a trail past all of the Burroughs peaks to the cleaver beyond (I forget it's name). There is a set of switchbacks from hell down off Burroughs into the White River Valley, then you follow the valley downstream a bit and there is another set of switchbacks back up onto Sunrise ridge. In itself that would be a rather short hike, but it can be combined with the other trails in the area.
Another more solitary one would be parking at Mowich Lake and making a loop into the Carbon River Valley using the Spray Park Trail, Seattle Park Trail, and the part of the Wonderland Trail along Carbon River and Ipsut Creek back to Mowich Lake. You'd probably even hit some snowfields, actually. The views are, again, spectacular on the southern part of that loop. (But then, it's hard not to have great views in MORA.) The northern part is river valleys and wooded draws, but Carbon River is in itself quite scenic. Again, zoom in GoogleMaps terrain view and you can see the trails marked. If that loop is too small you can make it bigger by adding the aptly-named Northern Loop Trail further east around Lake Ethel, Skyscraper Mountain, and Mystic Lake. This will again hook you into the Wonderland trail back to Mowich lake.