So this was a pretty short time in a place, similar to the amount of time I spent on the Brazilian side of Iguazu. I had roughly 2 full days in Panama City to explore the place and I did as much as I could on the first day. I stayed in Lemon Inn which is a pretty decent hostel.
Anyway, I did a hell of a lot of walking on the first day. From the hostel I walked over to Cinta Costera which is essentially a very long path by the coast of the city. You'll walk past all the incredible skyscrappers until you make your way to the next most interesting location, Casco Viejo. It's a really pretty part of town which has been declared as a world heritage site. You''ll find a lot of great restoration work done on churches and building but you'll still see some old decadent places too so it gives the place a very unique vibe. The main final stop of the day was the Amador Causeway which connects the city with the islands. I walked over here from Casco but you're probably better off (and safer) getting a taxi or bus over. Just before you get to the main road you can rent a bike for a few hours to go over and come back again which is exactly what I did.
After that I still had some walking to do but that was more so because of a few mistakes I made, primarily not having a metro card or having a passport to get one in Albrook station (I got here due to a local letting me use their card on the bus). So I'd recommend you getting a metro card early on. You can get them at most stations I believe and they're essential for travelling.
On my final proper day exploring, I went to the Panama Canal. A Colombian from the hostel joined me and helped me get a metro card. It was pretty useful and I got to practice some of my Spanish. For most people though, you'll need to get to Albrook station and from there, go to Mirafloras which will drop you directly at the Canal. It costs $15 to enter which is a lot I think. I found the Canal to be fine. Not really my thing and a lot of people but I suppose it was worth doing. I did enjoy the movie they showed and some of the history behind it.
And here are a few photos from my time there. Honestly it felt very similar to Singapore. So if you've been there, you'll know what to expect