The revamped Royal Opera House presides over Covent Garden like a super-cool grandmother. Enter via the colonnade of shops off the piazza to keep dry, or swan in via the main Bow Street entrance, comfortingly old-fashioned with its plush red carpets. The new parts of the House are all gleaming marble and glass. Take the stairs up to the magnificent refurbished Floral Hall, a tower of glass and steel with a circular bar smack in the center. Then, ride the escalators up to the Amphitheatre bar and gaze down like Caesar on the drinkers below. You can also join the poorer opera lovers out on the balcony at the back, enjoying fresh air and unique views of the piazza. The auditorium itself is a triumph of gold leaf over taste, but get a seat above the stalls level unless you like your orchestra LOUD. Tickets for performances can be hideously expensive, but Travelex Monday performances offer 100 of the best seats in the house, for about $18 each. Go to the Web site and enter the ballot for a maximum of two tickets, and you’ll know at least two weeks in advance if you’ve won. Exhibitions of costumes and other memorabilia at the Royal Opera House are free, and because the objects are dotted around all over the House, it’s a great way to nose around this famous building without spending a dime.