Hey, no problem. I'm always glad to provide as much info as possible. I'm lucky enough to have a Panamanian wife, so moving here was a lot easier for me than it is for most other people. Plus, even though Panama is growing at such a surprising rate, most companies here suck at putting info on the internet. It's not easy to gather good info from abroad.
I'm not familiar with the Balboa Resort, but it sounds like you're kind of locked in to a room there, meaning you'll want to stay close to the city. If you haven't already discovered this site, check this one out. I've never actually been on this bus, but they've started popping up everywhere around town. They're red double-decker buses that allow you to hop on and off at different sites all over the city. I know they go to the canal and some of the malls and stuff. It would be a lot easier than trying to find it all yourself. The site says their tickets are $29 per adult for a 24-hour ticket or $39 per adult for a 48-hour ticket. I'm not sure how long it would take you to do everything, but 2 days would probably be enough. Then maybe that would free you up to get outside the city a little bit during the rest of your week. Oh...the site for that tour is www.citysightseeingpty.com.
As far as beaches close to Panama City, the only one really close is Coronado, which is considered by some to be a little bit pricey, but it really is the most expat-friendly lifestyle option. In Coronado there are three major supermarkets, a nice clinic, plus expat hangouts and stuff already established. If you're just visiting, you might have a hard time getting to a beach, unless you're staying at a hotel or something inside the Coronado gates. Most beaches here are slightly controlled by the resorts. Coronado is a good place for you to visit because it's only about 45 minutes to an hour along the Pan-American Highway. It's easy to find if you're going to rent a car. You'll know you're there when you see a huge shopping center on the right hand side called The Village where you'll see a KFC and a Don Lee Chinese Food Restaurant. Then, right across the street, on the left, you'll see McDonald's and two other shopping centers. That's Coronado. The street between the two shopping centers on the left will take you into the actual neighborhoods.
There you can actually rent horses at the equestrian club (you'll see it on the left hand side as you travel down the street that leads to the Coronado main gate). I was there last weekend, and I think it was like $30 per half hour to rent a horse. A nice park called Bosque Seco (dry woods) has trails you can take the horses on. There's a golf club inside Coronado and a restaurant called Picasso's that hosts happy hour every Tuesdays and Fridays. I was there last Friday and the place was packed with American speakers. Friday is salsa dancing night.
If you're able to get away from the Balboa Resort for one night, call Karys and her husband Darin at this number: from the US: 305-671-3455 or their Panama cell phone: 507-6714-2991. They run a bed & breakfast in Coronado called Morgan's Paradise. We paid $100 for our room, which had a king-size bed, air conditioning, tv with dvd player, and hot water. They have a pool, jacuzzi, and a sauna on site. They only serve continental breakfast though, which isn't a big deal since there are so many restaurants in the area. The good thing about staying at the bed&breakfast is that it's inside the Coronado gates, which means you'll be able to easily check out the beaches, Picasso's happy hour, and whatever else you want.
The only other places that are close enough to drive to and get to your resort by the end of the night would maybe be El Valle, which is about 2 hours from the city, 1 hour from Coronado. That's supposed to be a really nice mountain community. I'm headed there later sometime in November. I've never been, but I've heard it's great.
Oh, on the Pan-American Highway, before you even reach Coronado, keep your eyes open for a community called Altos del Maria, on the right hand side of the road. You won't actually see the development from the road since it's kind of a mountain community, but you should see signs. I met a couple last week in Coronado, at a great Mexican restaurant called Cholo's, who were actually living in Altos del Maria (had just moved there) and visit Coronado to do grocery shopping and eat at all the restaurants. They said the agents at Altos were great and helped them get to know the area and find a place to live. Their website is: http://www.altosdelmaria.com/
That's all I can think of right now. I'll write again if I come up with anything else. Hope this helps a little bit.
Chris