Planning trip to Utah late May. Mother/daughter (not young but fit) Have 7 days. Coming via air. Would like to see Salt Lake City in addition to a few of the National Parks. Should we rent a car or go with tour? Enjoy horseback riding & rafting but are flexible as far as activities. Appreciate any suggestions.

It would be more of an adventure if you rent a car and explore the national parks on your own. Due to their popularity during high season, there will be timed-entry tickets (reservations required). There will be horseback-riding opportunities adjacent to Arches and Zion national parks (two premier national parks). I wouldn't ride for more than 1-2 hours or you will be bow-legged for a day (seriously, those horses are wide). But you might want to horseback-ride in the mts. east of Salt Lake City and see the mt. scenery. Of course, there is hiking, mt. biking and whitewater rafting. I would go for a 1/2 day whitewater rafting trip. A whole day may be too tiring. Will need reservations. A friend really recommends Goblin Valley State Park--national park quality without the crowds. Have fun!

If you want to ride and raft you almost surely will have to do this independently.

Thank you for the info.

Also, there is a public shuttle bus you can ride into Zion NP from Springdale and you don't need the timed-entry ticket (just pay the park entrance fee). Arches NP has private shuttles from Moab and tour buses.

A little more detail....
There are two shuttles

1. Town of Springdale public shuttle bus, that picks up passengers through the length of Springdale, and deposits you at the pedestrian entrance to the park. At busy times this shuttle can fill up so may need to wait for the next one...
2. Zion Canyon / NPS shuttle, that takes you from the visitor center (a short walk from where #1 drops you off, the length of Zion Canyon.

Our go-to hotel is Cable Mountain Lodge which is also right by the pedestrian entrance to the park, obviating the need to ride shuttle #1. I've never had a problem driving from that hotel into the town of Springdale & parking to dine or shop.

Good ideas but you also could head from SLC to Moab and visit Arches and Canyonlands. You could loop around and hit Bryce and/or Zion on the way back

Mesa Arch in Canyonlands

Delicate Arch in Arches with a couple of 70+ yos.

Absolutely rent a car and go. If you search this forum, you will find many trip reports and itineraries for this exact trip. You can search my user name and find trip reports (including lodging, dining, and hikes/activities) for all of the National Parks plus Escalante, Kanab, Page (Arizona) etc. Remember that you don't want to drive after dark--you will miss amazing scenery, there are many places where the cattle are "free range" which means they can be in the middle of the road, deer all over and you don't want to hit one of those either. May will be a wonderful time--not too hot and should have plenty of wild flowers. But that means you will definitely have to have reservations wherever you.

Your best place to raft will be out of Moab. For horseback riding--Ruby's Inn at Bryce has some good tours you can book.