If you approach from the east side, you will be in for a 2500' vertical (minimum) to go over a pass that is over 11,000' (Kearsarge, 11,760', Bishop 11,900' are two examples). Then down the other side. So there would be some vertical with distance. Your wife may find that challenging.
From the west side you would have a fair amount of vertical, too, with more mileage to the nice spots. If you are content to stay in a canyon bottom and not get to the high country, you could go to Paradise Valley from Roads End, it is not that bad to get to Paradise Valley. Not the spectacular high country scenery that I like, but certainly better than staying in town. The problem there is that the Woods Creek trailhead is also the start of the immensely popular Rae Lakes Loop, so permit availability is questionable and you will also see a lot of people.
You could go in at Mineral King in Sequoia and go to Franklin Lake or Mosquito Lake #2 (about six miles, 2500' vertical total), spend a day there exploring and relaxing, then come back down. Franklin is more scenic, Mosquito #2 has more solitude (you most likely will not see anyone there) but involves some easy cross country because there is no trail for the last part of the route between Mosquito #1 and Mosquito #2.
Emerald Lake is a nice spot (popular, too) and is about five miles and 2000' vertical from the trailhead at Wolverton. Permits can't be reserved for this trail, it's first-come-first-served when they open the permit office in the morning. Weekdays you have less competition. That would make a nice destination for an in-and-out route. Camping is restricted to specific campsites at Emerald Lake.
To be honest, three days with short miles/low vertical really limits your possibilities. If you could do four days, other possibilities would open up. One would be to go in on the Bubbs Creek trail and take two days to do the 4400' vertical over 13 miles to get to East Lake, which is a beautiful location. Then take your time coming back out. Bubbs Creek is also a popular trailhead, so it may be hard to get a permit at this point.
You could start at Florence Lake and take the JMT over two days to Evolution Valley/Evolution Basin for a four day out-and-back trip.
You could take two days to go over Bishop Pass to Dusy Basin, or over Kearsarge Pass to Kearsarge Lakes for four day out-and-back routes from the east side.
If you are used to humping big loads, the compromise that you may end up making is carrying a monster pack with most of the weight while your wife carries her sleeping bag and personal items. That way she could keep up with you a little more easily.
I have pictures and trip reports that include all of those areas if you want to see what they look like.
