Get to Garden of the Gods early. There's no cost of admission but the parking lots do fill up. We got there around the time the visitor center opened (9AM) and asked the best lot to park in, and by the time we parked we were one of the last cars to get a spot. This was the first weekend in March, so I'd imagine it will fill up even faster in the summer. I'd hike first and do the visitors center after.
This is the lot we parked in -
https://maps.app.goo.gl/TxAtEh8Lp9vqQd4E7It was great for doing the paved loop trail, and we decided to add on some of the outer loop trails to go down to the Siamese Twins rocks since the paved loop was pretty short and easy. Not a hard hike but the altitude did start getting to me after a while. The other parking lots we hiked by weren't bad but I'm glad we were in this one because it was at one end of the park. By the time we headed back towards the car around 11:30, the place was a zoo. Lots of people only do the paved trails, so the outer ones were a lot less busy.
The visitor's center was cool but not very helpful - they don't give out paper maps anymore so you'll have to download one and print it before you get there. They do have a cool 3D model of the park.
We saw everything we wanted to by noon and headed to Manitou Springs. The Manitou Cliff Dwellings museum is really cool and only takes about an hour to see everything. You can even walk through the old dwellings to see what the insides were like.
Our favorite little shop in Manitou was 'Colorado Art of Facts'. The rest of the shops are pretty generic gift shops, but this one had genuinely cool memorabilia like old original post cards from the early 1900s, etc.
If you want a great breakfast, 'The Pantry' in Green Mountain Falls is about 15 minutes from Manitou Springs up into the mountains near the Pikes Peak turnoff and was so good we went back for breakfast a second day in a row. Get the Cinnamon Roll French Toast and thank me later.