If staying on the Recinto: it is a pleasant, peaceful place, with flowers and humming birds, but rather dull and deserted. The motel is adequate (you can get a good night's sleep), but a bit dated. Take quick showers, because there isn't a lot of hot water, especially in the afternoon.
If you have come off an overnight flight, and aren't hungry when you arrive, it'd be worth having a rest for a couple of hours, so you have a bit of energy to explore the town in the late afternoon and have dinner in the evening. Don't expect to to be able to stay awake past 10pm local time if coming from the East.
If staying on the Recinto: basic food is provided in the motel kitchen/living room, but is limited to bread, eggs, water, milk, cereal, jam, tea, coffee. There is a hob, with pans, and basic cooking utensils. Its OK for a quick breakfast, but for lunch/dinner most people go to restaurants and/or get stuff in supermarkets (both being at least a 20 minute walk and its up hill on the way back). People leave stuff behind, so you'll find oil, spices etc that are not provided by AURA. The fridge is also full of random stuff, that people have left. You have no idea how long stuff has been hanging around (or if the owner is still around and planning to use it). The kitchen is tidy, although not top hygiene rating.
If staying on the Recinto: you can ask at reception to order taxi's, or - if closed - at the guard posts to take you to restaurants. Don't expect instant taxi arrival (might take ~30 minutes). If there are other observers staying at the motel they will probably be very happy to go out for dinner with you, so don't be afraid to ask them if you bump into anyone. If you do end up being on your own for dinner, don't be worried about that. La Serena is very friendly and very safe, although take usual precautions (don't leave bags where people can grab them and be especially careful with your passport - if you are staying at the Recinto, the safest place for your passport is in your motel room - the Recinto is protected by high fences and guards).
If staying on the Recinto: the Aura booked taxi drivers are excellent, but others in town might not recognize the name CTIO or even AURA. If you tell them its at Huanhuali and Juan Cisternas, they should know. There are some Spanish instructions on the CTIO webpage that you could print off. Also take the map (given to you when you get to the Recinto) when leaving the compound in case you need to show it to a taxi driver (also helps you not get lost if walking).
If staying in a hotel: You have the advantage being closer to shops and restaurants and beach, but disadvantage of being further from the shuttle bus to the mountain. You'll need to get a taxi up to the Recinto to get to the carry all to the mountain and it'd be worth asking Ximena CTIO to book that for you (since the local taxi drivers might not know where to go, see above).
DES observers usually stay at the La Serena Club Resort: http://www.clublaserena.com It is very nice, and there is a surf shop (with rental gear and instructions) directly opposite if you want to brave the waves. Disdvantage is that it is a 45 minute walk to the decent restaurants (further up the beach away from the town centre). This is being recommended by La Serena locals, but it'd be good to have a DES review if you stay there http://www.enjoy.cl/coquimbo/
Whatever you do (if you are not "tea total") you must have a Pisco Sour on your first day in Chile. If you end up not liking, then someone else in your group is sure to be happy to drink it for you.
If you have two ore more days in La Serena: book a day trip to the Isla Damas to see amazing wildlife - ask Ximena to help with the booking (and wear sun screan on the boat even if it is cloudy)
La Serena old town is good to wander about in for an hour or so. Old churches, small streets etc. The craft market (La Recova; marked on the AURA map) is interesting to wander about and has nice stuff to buy over a wide price range. Most stalls are market style, but there are some tiny indoor shops too that are worth exploring.
La Serena town beach is about a mile from the old town. It is not particularly a pleasant walk (not unpleasant either) between the two, so take a taxi. At the town beach you can paddle, see the old light house, visit a beach front cafe or rent some surf kit (from shack opposite Club Resort hotel). It is worth going to that area if you are short of time and that is going to be your only view of the Pacific.
La Serena north beach: compared to the town beach, it is more modern, more developed, more amenities (clubs, shops, restaurants), nicer sand, better people watching. From the Recinto expect to pay about $15 each way Before the Tsunami (09/15) Bakulic Beach was good (might be repaired by the time you go). Tololo Beef (near http://www.enjoy.cl/coquimbo/) is really good, even for vegetarians.
If you want to dance all night you can (there are several clubs in the north beach).