Many classic cities have the well-adorned cafes where even regardless of the need for food or drink, the agenda is just to be there and stay for a bit. It may be a mixed clientele of curious tourists, cool locals and richer people who are willing to pay to be there, but there's no point avoiding it just to stay away from the other tourists (keep in mind being away from tourists comes more down to season and day of the week rather than where you go I think).
Majestic Cafe is indeed majestic. Regal and beautifully decorated (on the inside at least) and with more history spanning back to 1921 than I could ever appreciate it for.
Coffee is coffee - I'm not an appreciator; it was something appropriate to have. However the Rabanadas Majestic-style was a wonderful sweet snack of warm bread cooked with honey and wine and topped with cinnamon sugar, nuts and dried fruit. An unexpectedly fantastic treat for any time of day or night. I didn't try this anywhere else, and from photos of other versions online, I think this is quite an immaculate and upmarket version. Would go back for this any day.