Well if you want para and snorkeling in March then I think you need to go to the Canaries and you probably need to go to the fake beaches down at playa de americas in Tenerife. Basically the Canaries are south near Africa, while the algarve is much further north in Europe.

If you want just the other things I'd go to the algarve. Great bike rides, beautiful beaches and walks.

beautiful walks, diving, lovely scenery, and veggie food can all be had in La Palma. Look to renting a house on the west coast. Car rental is also cheap. Black beaches, not golden sands but otherwise it should meet your requirements. Certainly, away from the one big resort near the airport it is not a party island.
for even more quiet look at La Gomera.

Go to Tenerife or any of the other Canary Islands in March as the weather is much better than Portugal. Please ignore any snide comments about fake beaches and tourist resorts. They are made by people who have either not been to the Canaries or were too lazy to leave the resorts. There is far more to the Canary Islands than tourism. Lanzarote, Fuerteventura and Gran Canaria have real beaches and all offer great snorkelling.

Consider Mogan in Gran Canaria, Playa Blanca in Lanzarote, Corralejo in Fuerteventura, Los Gigantes in Tenerife, or anywhere on the three western islands.

See this guide to snorkelling in Gran Canaria. It applies equally to all the Canary Islands: http://www.grancanariasunshine.com/2012/02/underwater-gran-canaria-scuba-and.html

As above if you are more focused on beach. If its walking then Algarve.

Portugal is beautiful, but in March the Canaries will be warmer.

In March I would head for Lanzarote, (I like Playa Blanca too, in fact I may well be but if I don't get there alternative is algarve in June)

The Atlantic is a chilly ocean but it fares far better around warmer Canaries.

Ok the flight is longer and Thomson Holidays, who seem to have the UK and German market share treat the airport like a cattle market and appear to group their departure flights to keep costs down. This leads to a very busy check in area.
But its a lovely place and as yet not totally spoilt.
If you choose Gran canaria Island, Maspalomas is nice. There are many horrible resort areas in Gran Canaria that I hated. Hiring a car is a great way to see the islands.

Good luck

Muck

In March the Algarve will be very quiet, probably quite cool and the sea will be freezing. A good deal of the restaurants, hotels etc. will not be open.

The Canaries are much further South and a good deal warmer and the tourist areas whilst being much quiter too, will be open for business. I like the Corralejo area of Fuerteventura where it will be a lot warmer. There are many restaurants who will help with Vegetarian food if you explain what you can't eat.

"fake beaches down at playa de americas" the natural beech of Canary is black, they ship this blond one in. Nothing wrong with that from a beech holiday point of view but...