If you're in Santiago, you should definitely go to Valparaíso/Viña del Mar. Spend a couple of days there, and you'll get the water. Valpo is a historic, 19th-century port city with beautiful views and architecture that oozes character (although it's rather scruffy, it's not unsafe.) Viña by contrast is a lovely, genteel beach resort.

La Paz is a fascinating city. The physical location in a crater in the Andes is stunning, and it's a unique mix of Spanish and indigenous culture, plus gorgeous colonial architecture. From there it's very easy to get to Copacabana on Lake Titicaca.

If you had more time I'd suggest you could drive or take a bus north from Santiago/Valpo to La Paz via Lake Chungará and the altiplano. But if you've only got about a week, then probably you'd want to fly from Santiago to another destination and divide your time up between those two bases.

Oh, and if you do go to Bolivia, don't drive. The road conditions are really bad, it takes forever to get anywhere, and the drivers are mostly insane. I'd take buses instead and let a professional worry about it.