The Vatican Museums will stay open until 11 p.m., with the last entrance at 9:30 p.m. You'll have to reserve a ticket online in advance; €14 ($19.70), plus a €4 ($5.60) online reservation fee.
Go museum-hopping: Ara Pacis Museum is architect Richard Meier's controversial modern glass home for a marble altar consecrated in 9 B.C.; the Capitoline Museums display a staggering collection of Roman statues and medieval and Renaissance art; and the Centrale Montemartini is a former power plant whose machinery sets off ancient statuary more recently acquired by the Capitoline Museums. Tickets for Ara Pacis are €6.50 ($9) and a combined ticket for the Capitoline Museums and Centrale Montemartini—valid for seven days—is €8.50 ($12).
Cap off the weekend with a moonlit stroll through the Colosseum and the Forum, €9 ($13) total.
If you plan to visit all these attractions, it's worth purchasing the Roma Pass. It costs €23 ($33) and gets you free admission to the first two attractions visited, plus discounts at subsequent attractions and select events, and unlimited rides on public transportation for three consecutive days. Maximize the value of the card by visiting two expensive attractions first. Get more details and purchase the card at romapass.it.