I'm a frequent visitor to Lake Harriet, and find that it has a good balance of business and space compared to the other lakes in the Minneapolis chain of lakes. It's far enough from Uptown that it has less busy feel, yet has lots to offer. Check out a concert at its bandshell most summer evenings, stroll through the neighboring rose gardens, throw a Frisbee or fly a kite in the open area between the lake and the rose gardens, run/walk the ~3 mile circle around the lake, ride the historic trolley, grab a snack or meal at the concession stand, or visit the Linden Hills retail/restaurant only a block or two off the lake on the West side.
If being in the water is for you, there are two beaches (one on the North end and one on the Southeast side).
If being on the water is for you, there's a bike, canoe, kayak, etc. rental shack (weather permitting). If there's a breeze you'll find several sailboats out on the water. There is also a public boat ramp to launch your own sail or non-motorized boat.
The North end of the lake connects to Lake Calhoun via bike or walking trails neat the bandshell. The South end connects with Minnehaha creek walking and biking trials near the SE beach. Both are part of the grand rounds trail system.
Parking on the parkway is free (the lots now have meters but are usually open except during peak times).
Bring a picnic basket and stay for the afternoon!