Moomba Beach, Eagle Beach - just about anywhere I can wiggle my toes in the sand and enjoy an ice cold Bright
If you are staying in the Palm Beach area here are a few walkable user friendly places that I think would be fun to go to even if I were on my own:
Salt & Pepper @ the bar - decent food and nice bartenders Cafe Rembrandt's @ the bar - great food and amazingly nice bartenders (Dany is my favorite and is a manager if you need help/assistance) Busters - decent food and great staff. Marvin and Jose are the two bartenders that I know the best but you really can't go wrong with anyone there Smokey Joe's @ the bar - good food and great staff (I know Andres the best - for years actually - he will never steer you wrong.
arashi & boca catalina
la cabana pata pata bar
one thing i know...you're gonna fall in love with aruba & i'll bet your next trip there will be longer!!!! we've always rented a jeep but this forum always says great things about the cabs & bus. i hope you have a wonderful time & can't wait to hear your thoughts when you return
Cabs --> super easy. They're sitting outside the resorts. Restaurants will call for a cab for you when you're paying. You can also hail cabs downtown. They generally have to pull off the main street to pick you up, so it's better to stand by a corner. The cab drivers are very friendly.
Regarding bikes, I think I've seen some at a couple of resorts for their guests, but I can't say that for certain. You're within easy walking distance to tons of restaurants and shopping from Palm Beach. If you want to go site seeing around the island, that's a different question. You might want to look into some of the sight seeing tours in that case.