UPDATE - checking Google Maps, I see there is a bus running from Long Beach to Anaheim for $3-something. You know how much I hate buses... Lol
The Metrorail Blue is a light rail that runs from Long Beach to downtown LA. From downtown LA, I can catch a Metrolink commuter train to Anaheim. It's a much longer trip that requires several transfers.
Here's the deal, I can take the light rail blue to downtown, get a hotel in that area, fill my itinerary with things in that area for the days of 8/27 and 8/28, spending the night of 8/27 (and maybe 8/28) in that area. On either the night of 8/28 or the morning of 8/29, I can then take the Metrolink commuter train from downtown LA to Anaheim and spending the day at DL. Or I could just stay at downtown LA the whole time, taking Metrolink back and forth to Anaheim on the 28th, leaving the 27th and 29th free to explore Greater LA...