What are the "driest" places in Ecuador around March

You've essentially asked where is it dry except where it's dry? Galapagos and coastal provinces are usually dry around this time of the year. The rest of the country expects moderately rainy weather in March which means a higher probability of rain. You may be lucky some days, while others not.

Jungle trips are possible and you should expect rain there any day of the year. Some times it just rains for short periods, other times for hours. Paths get really muddy and you will be often provided with rain boots but do bring your own waterproof jacket or poncho.

For less wet rain-forest, head as far north as possible. Tours starting from reserves around Coca are possibly your best bet. Note that venturing too far north is known to be unsafe, so be careful.

This is incorrect (Itai) on a couple of levels. I work in the northern coastal provinces and they are truly soaking at this time of year. See below, March, April, May is actually the wettest time of the year (this is the airport in Esmeraldas on the coast) in the northern coastal regions.

1. Head to Salinas, it "sticks" out into the frigid Humboldt current and is bone dry this time of year, it is actually desert land use in some places out there and not only dry but a great beach. This is actually peak season in Salinas and when people go, the climate this time of year is just stellar. It basically almost never rains!

2. The rain-forest rainfall is remarkably consistent, check the map. It is not drier north. A better way to say it would be the center is wetter but the north is as wet as the south.

3. Itai is correct though on the north rain-forest being dicey. I would head south to Macas and take a trip out to Shaur country or head out from Quito to Tena as this is safe but do not go much further north than this.

I'll give you my rule of thumb for the wet season on the coast, first time I've told anyone. Find a town called Bahia de Caraquez. North of this you are getting wetter and wetter in the wet season. South of this you are getting dryer and dryer in the wet season. Going north once you hit Pedernales you are out of the transition zone and fully in the wet zone. Going south once you hit Machalilla you are out of the transition zone and generally pretty dry after that.

So draw a line between Pedernales and Machalilla and write "transition". North of it "wet" and south of it "dry".

It is fascinating as it all depends if you are in the "Humboldt / Peru" current zone (cold dry) or the Equatorial Counter Current Zone (hot, wet, humid) and they shift, so this is why I have a transition zone. Bahia is right where those red lines end!