You can legally open carry anywhere that doesn't have security/metal detection capabilities and other federally banned buildings. However, Denver city and county (as well as the park systems owned by them) are also off limits due to a court ruling after state preemption.
You could apply, however, because you're not a resident you will likely be denied for a permit. There is actually an ongoing lawsuit against Denver because of their OC ban and the fact that Colorado doesn't offer permits for people who aren't residents of Colorado already.
Generally speaking, if a business has a "no firearms" sign they will enforce it by calling the cops, not asking you to leave. If you are asked, or escorted out, you must leave or be charged with trespassing.
The only municipality that has a legal OC ban is Denver City/County and all things owned by them. Nevertheless, that doesn't mean that you won't be hassled in other parts of Colorado. Castle Rock has had some issues and I believe that Telluride believes they can legally ban OC, but to the best of my knowledge, there have been no test cases.
RMGO is a great organization that truly fights for the rights of gun owners. They also offer many different tools that are very useful to people who carry, concealed or openly.