Not much for beautiful beaches in the north of St. Lucia, but then again beauty is in the eye of the beholder as they say.
Up north you have:
Reduit Beach in Rodney Bay. It's a narrow beach and does get crowded cruise ships are in. The surf can be pretty rough if the northern swells are running. It has the most infrastructure as far as bars and restaurants.
At Pigeon Point, you can go into the park, there is a small beach there and a nice local restaurant Jamb Du Bios.
Outside the park is my favorite in the north, there are two small local restaurants with good fresh food and drinks, all at local prices; 2 Chairmen's Reserve rum drinks for 8 EC, 2 Pitons for 7 EC.
Chairs and umbrellas are available for rent at each. Let them know you're staying local and not on a cruise and you may be able to negotiate a better price.
There is also a beach on the Atlantic side at Cas em Bas. Marjorie's (made famous by Amy Winehouse)is the only restaurant there and her prices reflect that. The beach can sometimes have seaweed since it is facing the ocean, however a small reef just offshore keeps the breakers down. There is a very good kite surfing school there if you would like to try it.
There is a beach just north of Gros Islet before the big resorts. Nice for swimming, but no services; however it's just a short walk to get a drink or meal in town.
Some snorkeling at Pigeon Point and Cas em Bas, but nothing to write home about.
They have recently developed Viggie Beach near the small airport outside of Castries. I haven't been there yet but have heard there are local snack bars and rum shops there. Passing by, it looks like a nice long beach.
All the beaches in St. Lucia are public.
Day passes at the larger resorts run something like $100 per person I think.