While renting a car for the duration of the trip may be the easiest and most convenient option, public transportation and ride-sharing services like Lyft and Uber are also available. Expect to spend around $150-200 for a week of car rental, or between $50-100/day for ride-sharing services depending on distance and time of day.
If you have more time, consider taking a day trip to Joshua Tree National Park or visiting some of the beach cities to the north of LA, such as Malibu or Santa Barbara. If you have less time, consider skipping Knott's Berry Farm or Universal Studios and spending a day at the beach instead.
The closest airport to Artesia is Long Beach Airport (LGB), located 14 miles from the city center. Other nearby airports include Los Angeles International Airport (LAX) and John Wayne Airport (SNA), both located approximately 30 miles from Artesia.