If you've not seen Giant Sequoias, you should do that, Tuolumne Grove or perhaps Merced Grove. The Pohono suggestion at 15 mi seems too ambitious to me if your previous best is 7 mi easy/moderate. The longest I'd recommend for you is Glacier Point down the Panorama trail is about 9 mi and mostly downhill if you can get a ticket up to Glacier Point on the shuttle.
Since it's your first time, see all the classic sights in the Valley: Vernal/Nevada Falls (as Jim suggested, 5.5 mi steep round trip climb, but you can stop at Vernal if it's too much); Yosemite Falls; Bridalveil Falls; Mirror Lake (and perhaps the trail beyond). Consider climbing up to Columbia Rock and Oh My Gosh Point (steep, ~3 mi round trip). Try to get to the tunnel views on 41 and 120 and stop at Valley View too.
With 4 days, take a drive up to Tuolumne Meadows at least one of the days. There are several easy/moderate hikes within your previous mileage range there: either north or south on the PCT along the river (both are flat); hike around Tenaya Lake (flat); Elizabeth Lake (moderate 5 mi round trip); Cathedral Lakes (moderate 7 mi round trip); etc.
Check out (and maybe print out) the Hiking Maps for the Valley at
https://www.nps.gov/yose/planyourvisit/ ... hikes1.pdf and Tuolumne Meadows at
https://www.nps.gov/yose/planyourvisit/ ... mhikes.pdf .