While places are relatively close to each other and walkable in Lakewood, for day trips, it's best to rental a car. Expect downtown parking to be expensive, so consider parking at a park-and-ride and using public transportation to explore.
For shorter trips, consider skipping the day trip to Disneyland and spending that time exploring more of Lakewood. Alternatively, those with more time should visit other nearby destinations such as the famous Venice Beach Boardwalk in Santa Monica or go hiking in Runyon Canyon Park.