I am in the opposite boat as you, with many DLR trips and first trip to WDW next week. Unlike many others, I am a big fan of DLR in the summertime.
June will be a little milder than July or August. I wouldn't let that be the deciding factor though. For the most part, all three months will be warm. We went early August in 2005, and all of the days were 82-85 degrees. We got lucky. I have been there when it is 100 degrees, and still had a great time. No humidity in CA makes it a much different experience than FL in the summer.
So here is a rundown of some advice for you to peruse, specifically for 2006:
1. Late June this year will have some unique disruptions. POTC will reopen June 24, and the movie premiere will be held June 24.
Check out this article:
http://www.miceage.com/allutz/al041806a.htm
POTC is a personal favorite, and by almost everyone's account much better at DL than MK. So I would not go before June 24.
The June 24 event will also disrupt Fantasmic performances, so pay attention to that.
2. DLR draws more locals than WDW, which means weekends are always busier than weekdays. And holiday weekends are busier still. That means stay away from July 4.
We plan our days as far from weekends as possible. Last August we had a four day trip, and went Mon-Thurs.
3. I have read up on WDW a lot, and the park dynamics at DLR are much different than WDW. One obvious difference is that there are two parks instead of four. But the two parks are so physically close to each other (1 minute walk gate to gate) that it is easy to hop back and forth multiple times if you want. At WDW there is a significant time loss to park hop, and you need transportation to do it.
In addition, the easy parkhopping makes DCA look less like a separate park and more like an extension of DL - sort of like CaliforniaLand. We treat DL and DCA as one big park, instead of two. But the fact there are two parks has implications on things like FastPass - the systems are not connected between the parks.
Further, the closeness of the hotels makes it even easier to take afternoon breaks. We stayed at a good neighbor hotel last year that was a five minute walk from the DLR gate. We never got in our car, or on a bus or tram all week. Just used our feet, which means no waiting for transportation.
So, tips for touring DLR are similar to WDW. Arrive early (15-30 minutes before the park opens), collect FastPasses throughout the morning for later use, take 3-6 hour break mid-day to your swimming pool and air-conditioned hotel room (and take a nap), return to the parks late afternoon or early evening with all of your FastPasses, and stay until midnight.
4. The Early Entry (EE) program at DL (DCA does not have one formally) plays a big role in traffic patterns. EE lets selected guests into DL one hour early into selected rides in FantasyLand and TomorrowLand (Mon/Tue/Thurs/Sat). Most of the FantasyLand rides are slow loaders, so if you show up in FantasyLand on an EE day (and you do not have EE that day) the lines will be long before you ever get into the parks. Moral of the story? Only do FantasyLand during EE when you have EE, or first thing on a non-EE day.
Because Wed is farthest from the weekend and does not have EE, it is the absolute best day to go to DL. Do your DCA day or days when DL has EE.
5. The DLR FastPass system has idiosyncracies that do not exist at WDW. If you learn these, you can simplify picking up FastPasses.
Read my DLR FastPass thesis here:
http://www.disboards.com/showthread.php?t=885132
6. If you stay at a DLR hotel and book thru
AAA, you can get Enhanced FastPass. Read about EFP here:
http://mousepad.mouseplanet.com/showthread.php?t=43193
Note that I would only get EFP if I was already planning to stay at a DLR hotel. I would not pay for a DLR hotel just to get this perk - which I think is overrated.
7. The Remember Dreams Come True fireworks.laser/special effects show is just awesome - do not miss it. It was designed especially for the DL 50th anniversary. But you will only get the full effect if you are close enough to the castle to see all the effects. This means that tons and tons of people jam into the hub to see it. Do some research on this. We got a good spot about one hour before it started.
Put it altogether and what do you get? Well, some time between June 24 and July 4 might be good, or anytime after July 4. The park hours and shows will be maxed out during the whole time. So it will all be fairly equal as far as crowds.
But I would not let crowds scare you. By getting to the parks early, taking breaks, and going back in the evening with FastPasses, we never waited more that 20 minutes for any ride. Usually it was less than 10 minutes. And we rode everything we wanted multiple times and saw all the shows and parades.