I think user "options" are always the best :)
- Do uptime monitoring alone from secondary locations more frequently
I like this but I'd add to make this configurable. Meaning you would have the choice of primary interval and then secondary round robin interval.
- Do one another secondary location check along with primary location
If the first option was implemented this wouldn't be needed.
- Allow to define additional primary locations for a monitor and do polling on configured intervals
Think this is a good option as well.
- As you suggested provide current option along with option to choose round robin polling option
If only one were to be implemented I would vote for having a primary check with its own interval and then round robin check of all secondaries with their own interval. IE Primary = California every 1 minute and Secondary = Tokyo, Australia, London etc ever 3 minutes meaning each (in a 3 secondary scenario) would get hit every 9 minutes.