DEN is great and you'll want to talk to COS for the Class C anyway (very very busy airspace even around it on either side), they'll hand you off over the "low" ridge where 8500' is comfortable or even 9500' (Palmer Divide if you remember that), to DEN TRACON. You'll have to bend West a bit to avoid KAPA airspace.
Look for Chatfield Reservoir on the sectional straight west of KAPA - split the goal-posts of that and KAPA airspace to the east and then angle over toward I-25 watching the Bravo overhang altitudes there.
The southwest practice area is bounded by Chatfield on the north and extends straight south of it a few miles. Students in there doing maneuvers will be on 122.75. It's not charted. So don't plow straight toward Chatfield from the south.
Expect going to BJC from the south DEN TRACON will say "remain clear of the Class Bravo airspace VFR West of I-25", but they're great about traffic advisories and they'll still give you a squawk since that's a "funnel" between the West edge of the Bravo and the foothills with a lot of opposite direction traffic north-south. Actually they'll maybe let you keep your COS squawk if COS entered you in all the way to BJC.
If COS is busy, one annoying thing they can do is drop you, "squawk 1200, RADAR service terminated" right at the Palmer Divide. Have DEN freq handy or ask the COS controller to give it, since you're about to go right into the Bravo if you're high. Further West the Bravo is higher.
Right past downtown along I-25 is cool if you stay with the Interstate, just watch the lower Bravo altitudes and all the major sports stadiums are downtown so TFRs do pop regularly there.
Locals and helicopters sometimes squeeze up the *east* side of downtown which is even lower for the Bravo, but I don't recommend it unless you know where all the golf courses are, as they're your only option for an emergency landing on that side and there's a ton of them, but you're also down at 1000' AGL and pretty low. Not much time to aim for one. The West side has less options for landing actually... But you're higher and have more time.
The "West of the Interstate" route staying near I-25 northbound will put you on about a 3 mile left base for 29L/R at KBJC which is typically the direction they're landing, or an easy left turn to an extended right downwind for the opposite direction.
As far as Steamboat goes, Corona Pass (it's charted as Rollins Pass on the sectional - old naming battle that made it's way to the chart) just northwest of BJC, then up towards Kremmling and over Rabbit Ears pass into Steamboat, typically.
Corona is a long slog up for most of us without turbos and you hope DEN will let you climb through the Bravo. If not you may be shuttle climbing to get over it from the East. The terrain can outclimb most aircraft but the approach to the pass is wide and lots of room to shuttle climb back and forth.
Rabbit Ears is often fogged/clouded in and you can't go that day to Steamboat via that route. Pretty consistent crap weather visibility wise at Rabbit Ears if there's any moisture being pushed upslope from the West on the Steamboat side. You can get stuck in Steamboat by that phenomenon too. Rabbit Ears collects clouds and precipitation. Both sides can be gorgeous and the pass totally socked in. An old CFI friend has a photo of the rock outcropping the pass gets it's name from, and his comment is "I finally got a good photo without any clouds in it that day!"
