Palm Springs (60km east) — The desert resort city is an easy drive east on I-10. Mid-century modern architecture, a thriving restaurant scene, the Palm Springs Aerial Tramway, and easy access to Joshua Tree National Park make it the most popular day trip from Riverside.
Big Bear Lake (60km north) — A mountain lake at 2,000 metres elevation in the San Bernardino Mountains. In summer it is a cool escape from the valley heat; in winter there is skiing. The drive up is scenic, and the village around the lake is pleasant for a few hours.
Joshua Tree National Park (90km east) — Surreal desert landscape of boulder formations and the distinctive Joshua trees. The park straddles the Mojave and Colorado deserts and is best visited in spring (wildflowers) or autumn. Combine with a Palm Springs stop on the same day.
Los Angeles (90km west) — The full range: LACMA, the Getty Center, the Getty Villa, Hollywood, the coast at Santa Monica, the food in East LA. Traffic makes it work best on a weekend morning or a trip timed around Metrolink, which runs back to Riverside in the evening.