Hey there,
I've lived in Abu Dhabi for the past 7 years, and at the Hilton Capital Grand in Abu Dhabi for the past 8 months. I've stayed at almost all Hilton properties in the UAE, and I recommend you the Conrad Dubai (more expensive, fancy restaurants, nice pool area, beautiful rooms, suite upgrades, excellent lounge and breakfast at the restaurant for Diamonds). Second option would be the Hilton The Walk, which is not so fancy, but it's located at the beach and more to walk around. The Conrad would require taxis for everything, except a very nice Irish bar across the street called McGettigans. For such a short trip, you can do the Burj Khalifa Observatory, a Desert Safari with Dinner (see Arabian Adventures), a Hot Air Baloon Sunrise trip. Maybe you can stay 2 nights in Dubai and one in Abu Dhabi, where you can do afternoon tea at Emirates Palace (AED 260 per set - for two one set is more then enough, nice ambiance with a piano player etc) followed by sunset drinks at Ray's Bar across the street (62nd floor Jumeirah Etihad Towers - best views in the UAE). In Abu Dhabi, go for the Hilton Abu Dhabi Corniche, good location, standard executive room upgrades, nice Diamond recognition, good lounge and also breakfast at the restaurant for Diamonds.