While in Panama City, I would strongly recommend NOT renting a car and trying to drive. The reasons why a lot more than just "traffic sucks" ... which is very true. Taxis in Panama City are plentiful and, by U.S. standards, very cheap. But, they don't have meters. They charge by a zone system (for which none of the drivers have a map). So, when getting a taxi follow two important rules. #1, never get into a cab until you've settled on a price for where you're going, and #2, never get a taxi in front of a hotel or a restaurant -- they charge more than double. Example: going from Torres de Alba in El Congrejo to Miraflores, the taxi wanted $15. Crossing the street and asking the first taxi that pulled over (within 15 seconds),the same trip was $7.
I've never had problem going to the ruins of Panama Viejo at any time. But, keep in mind that there is not a lot shade, and in the afternoon, it's much hotter. When you go, the admission covers both the ruins and the archiological museum. They are not next to each other. The museum is actually about a mile or so away. So, make arrangements with your taxi to take you to Panama Viejo, pick you up 45 minutes later (that's all the time you'll need), take you to the museum and pick you up 30 minutes later. The reason to make these arrangments is because there aren't many taxis at Panama Viejo or the museum.
Also, figure that whatever your on-line quote for the rental car ... double it for the actual cost. There are a number of charges not included in the on-line price ... $18 or $22 per day mandatory liability insurance, plus taxes, plus fees.
IMHO, the restaurants on Amador are great for a drink and ceviche and the view at night, but very mediocre and overpriced for meals. There are much better restaurants in the city. For example --
Traditional Panamanian food -- El Trapiche on Via Argentina. Very inexpensive. Go across the street to Manolo's Chorreria for dessert.
Okay traditional Panamanian food, but a very entertaining show to go with it -- Las Tinajas just off Ave. Frederico Boyd. The show is Panamanian folk music and traditional dance. Call for reservations ahead of time.
Seafood - the Mercado de Mariscos (fisherman's market) during the day an Siete Mares at night (El Cangrejo district, just off Via Argentina).
Steaks - Martin Fierro on Ave. Eusebio Morales in El Cangrejo -- excellent Argentinian beef.
El Bodegon - San Francisco district - the best Spanish cuisine west of Sevilla.