Distance from my hotel

Looks like the trolley goes right by your hotel on Ala Wai, but doesn't stop -- unless it makes unscheduled stops, you'll have to catch it on Kalakaua. Still, only the Red Line goes as far as downtown Honolulu, and the ToysRUs places are further ewa (west) -- in Aiea and Pearl City. Probably better to take TheBus.

Here's the trolley maps:http://www.waikikitrolley.com/trolley-lines/red-line.html

Depending on what you are looking for at Toys R Us, you might not need to make the special trip. There is a Wal-mart behind the Ala Moana Mall (a definite stop for the Waikiki Trolley) that has a huge toy department and good beach selection. If you are just looking for some sand toys, stop in to any ABC store (there is at least one on every block in Waikiki) and pick up the $10 sand toy special. If you really need to head to Toys R Us, it is located near the Lower Side of Pearlridge Mall. Work with your hotel front desk and they might have some ideas on ways to get you there, otherwise, like Nene said, the Bus is probably your best bet.

I forgot about the Wal-Mart -- great suggestion. (If you go looking for it, don't expect a 10-acre parking lot like the ones on the mainland -- Wal-Mart and Sam's Club are attached to a big parking garage.) Anything there will cost a lot less than it will in Waikiki, plus it's worth visiting just to see how different it is from the ones on the mainland.