Hi, welcome to the forum.
Garden of the Gods is off limits, designated as wildlife habitat. Peterson AFB/KCOS on the east (class C), Ft Carson (Class D) of the south, and USAFA (class D/G on the north). A really wonderful place to help learn flying is Palmer Lake. Very drone friendly area. Catch the lake and the trains! GOG is declared as wildlife habitat and the City of Colorado Springs will not grant permission to fly in the GOG. Same for Bear Creek Park! And, Palmer Park. You certainly may TO/L outside the parks (with land owners' permission), but good luck on that. Flying over from outside the parks will not benefit anyone as you will quite easily lose visual observation very quickly. I would recommend you start out low and slow in one of the many other city parks. Near me I prefer Wildflower Park, I just walk from the house.
Brush up on DJI unlocking procedures if case you get closer to Springs Air Port, Class C. Really would recommend some of the smaller parks to help gain familiarity of the drone and controls, not to mention the DJI unlocking procedures.
USAF ACADEMY AFLD(AFF)(KAFF)10 N UTC–7(–6DT)N38º58.40 ́W104º49.20 ́AIRPORT REMARKS: Afld opr hrs and Class D services avbl SR or 1245Z‡ (whichever is later) to SS Mon–Fri, 1430Z‡ to 2130Z‡ Sat, excluding Sun & hol. Afld official bus only. See Special Notices—U.S. Air Force Academy. AIRSPACE: CLASS D airspace SR–SS; other times CLASS G..
Butts Airfield (Ft Carson) on the south: AIRSPACE: CLASS D svc Fri–Mon 1200–0600Z‡, Tue–Thur 1100–0600Z‡, clsd New Years day, Thanksgiving, and Christmas; other times CLASS G..
COS: AIRSPACE: CLASS C svc ctc APP CON