Sorry to hear of your loss...
Since you didn't indicate the portion of Salt Lake City in which you wish to stay, below is information on a couple of campgrounds within 30-60 minutes of the city center.
There is a campground in Jordanelle State Park in Park City, but I suspect that location may be too inconvenient, considering the nature of your trip.
Willard Bay State Park - Willard Creek Campground
900 W 650 N
GPS: 41° 25.158'N, 112° 3.171'W
Paved interior roads and parking pads. Campsites have metal patio cover over metal picnic tables on concrete pad, with BBQ stand and fire ring. Some sites have shade trees and others are in full sun. Flush toilets, showers, dump station. Some RV sites have full hookups.
Lots of bugs in warm weather due to proximity to lake. When we were there, a sign at the entrance indicated campground was scheduled to be fogged for mosquitos.
OK for an overnight stay; but, besides bugs, there is lots of highway noise from I-84/I-15, which is immediately adjacent to the campground. Campground was full for Memorial Day holiday weekend 2014, because of the "grand re-opening" of this state park after temporary closure for partial refurbishment.
RATES: Full hookups $28, tent sites $20.
Brigham City/Perry South KOA
1040 West 3600 South
Brigham City, UT 84302
GPS: 41° 26.694'N, 112° 2.449'W
Gravel interior roads and parking pads. Older property with large shade trees and swimming pool. Appears to have typical KOA amenities.
Website: Brigham City / Perry South KOA | Camping in Utah | KOA Campgrounds
RATES: Full hookups $40-50.
Note: We have never been to this KOA.
Utah Lake State Park Campground
4400 West Center Street
Provo, UT 84601
GPS: 40° 14.358'N, 111° 44.150'W
Paved interior roads & parking pads. Covered picnic tables. Can be very windy at times. Lots of bugs in warm weather, due to proximity to lake.
RATES: Water & electric $25, additional vehicle $10.