La Paz sits in an extraordinary position for day trips. Within two to three hours in almost any direction, you can reach ruins older than Rome, salt flats the size of a small country, and jungle roads that drop three vertical kilometres in a single ride. Most visitors stay three or four days in the city and barely scratch the surface.
The closest major excursion is Tiwanaku, 70 kilometres west on the altiplano. The ruins of this pre-Inca capital take about an hour and a half to reach by bus or shared taxi from La Paz's Cemetery district. Most people do it in half a day, but combining it with a stop at Tiahaunaco village for lunch stretches it comfortably to a full day. See the separate Tiwanaku entry for what you'll find there.
Death Road cycling is a full-day affair departing early morning. Operators pick you up from your hotel, drive you up to La Cumbre pass at 4,700 metres, and then hand you a mountain bike for the descent to Coroico at around 1,200 metres. The ride itself takes four to five hours depending on your group; you're back in La Paz by early evening. See the Death Road entry for how to choose an operator and what to expect.
Lake Titicaca and Copacabana make for a long but very doable day trip — 3.5 hours each way by bus, with time to walk the lakeside, eat trout, and take a boat out toward Isla del Sol. Many people stay overnight in Copacabana to catch the morning light on the lake, which is the better plan. The Salar de Uyuni, while often listed as a day trip, is genuinely better done as a two- or three-night journey south — either by overnight bus or a short flight to Uyuni town.