Arica ... small town on the edge of the Atacamba desert. Good place to shop for handicrafts, painted gourds, etc. short sojourns by taxi into the desert are worth while. I really enjoyed this place. Felt safe here.
Lima ... big, busy, congested and somewhat dangerous. Suggest that you hire a car with guide/driver on the pier and arrange your own tour. There will be booths set up. We had a group of 8 and hired a mini-bus that could hold about 14 for about $30 for all day/each. Included driver and English speaking guide. We went to some interesting Inca ruins about 1.5 hours south of town and a couple of museums.
I've been to CR several times but not Puerto Limon. Nature foto trips and river rafting are recommended for CR in general, but not sure of availability in Limon. Petty theft can be a problem, hold onto your camera.