Sandra, I can only generally speak to Panama for your request. I was just in Panama. You don't mention where you might want to go in Panama but I was in Panama City, Bocos del Toro, and Boquete. In Panama City, there are a number of reasonably good hotels, though not particularly cheap (well, by American standards but with the Euro vs. dollar situation you may find it all cheap!). Chain hotels would include Radisson, Crowne Plaza, InterContinental, Wyndham Veneto, Four Points by Sheraton and others. I personally am going on the budget route, so all of these were out of my league for this particular trip. However, I took a look at a few just to get a feel for some of these hotels for another time. I think you would do well at either Radisson or Four Points for location and nice rooms. The Radisson appeared to be running around $200/night and Four Points at around $160/night. These are both in the downtown area with attractions and restaurants nearby. You may also look to Country Inn and Suites by the Canal. Rates appeared to run around $139 and you're by the Causeway, which is a little outside of downtown but the Causeway is a great place to walk. From there, you should be able to get a cab for not more than $3-4 into downtown. All of these hotels should be listed on Travelocity or Expedia.
If you're looking for less expensive, you'll be looking for independent hotels. At that point, quality may be good but may also vary wildly. You may check out Suites Ambassador, http://www.suitesambassador.com.pa/en-panama.php. It was near where I stayed and you'll have restaurants, some shops, and casinos within walking distance. It appeared more basic but less expensive, around $80-90/night. Ambassador is in the El Congrejo neighborhood, not near the water, but near downtown.
In Bocos, it is very beautiful being on the island, though more laid back and rustic. If you want all suites and full-inclusive resorts, don't go to Bocas. Tropical Suites appears to be the best of the possible choices, running $160-225/night depending on seaside view or island view. You're also near Bocas Town. Swans Cay was around $80/night, but rooms seemed very dark, not very good windows or lighting. You can go to www.bocas-del-toro.org.
Boquete is a small town in the mountains of northern Panama. Temperatures will be cooler than in Panama City or Bocas. Panamonte Inn is probably the best of the hotel options in Boquete, around $90-100/night, very much on the B&B/historic inn feel, but appeared to be recently remodeled. Lots of more basic options too.
I can tell you the city of David has really nothing for the tourist, at least from what I saw. It's basically a passthrough town for planes or buses. Let me know if you need more info...I'll offer what I can.
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