Storing bags somewhere on the morning of arrival sounds difficult and not very secure, so I probably wouldn't do that option. Also, there's a fair amount of walking/steps/etc at Cristo Redentor and the Sugarloaf so you might want to do them on a day where you're fresh, rather than after traveling.
Taking the subway into the city might be a good idea if street traffic is bad. If traffic isn't bad, a taxi/Uber isn't going to break the bank and is probably the most efficient way to get to the sights so you can focus on them rather than the transportation part.
Another thing you could do is email the concierge at the Grand Club in advance and see if there are any tours they could schedule you on that would take you to the sights. You might still have to taxi to meet the tour, but once on the tour you wouldn't have to worry about transport.