Reddit mentions: The best swimming equipment bags

Swim Buoy Safety Tow Float 28 Litres Dry Bag by WildPaces High Visibility Orange ideal for Open Water Swimming SUP Kayaking Fishing Snorkeling https://www.amazon.com/dp/B0752TP2VQ/

Something like this

Edited to remove apparent referral through Amazon app

I use the Tyr Alliance Team Mini backpack. It's absolutely cavernous inside, has a separate shoe pouch, an inside pouch that fits my laptop, two large side pouches which when unzipped act as nice bottle holders. Construction is pretty solid, although the inside pouch where you can fit a laptop isn't the most durable, but I put my laptop in a padded sleeve so it's a non-issue. The price is good too.

Note that I use the mini version. There is a larger version (Tyr Alliance Team II) that is made for swimmers to hold flippers, a wetsuit, towels, you name it. It's quite big, hence why I use the mini (which is actually the kid's version). Google some images for size reference.

How many external compartments are you looking for?
Here are some I found that fit your description:

• Kelty - Redwing 32 - 32 liters at $100. If this is too small, they also have a 40 or 44 liter version, but it will cost most.
  
• Everest - Hiking Backpack - 48 liters at $30, maybe a bit too big.
  
• Fuel - Top Loader Backpack - 33 liters at $23
  
• Fuel - Multi-Pocket Cargo Backpack - Just like the one above, but has more external pockets. Be careful with this one though, reviews aren't the best. $25
  
• Under Armour - Storm Undeniable II Backpack - 35 liters at $46.98
  
• Oakley - Enduro - 30 liters at $75.66
  
• Osprey - Tempest - 30 liters for $116
  
  Edit: I think I found the keywords you should look up: "swimmer backpack". A lot of them of top-loading and have external compartments.
  
  Here are a few I found:
  
  
• MIER - Large Sport backpack - 40L at $35
  
• Speedo - Large Teemster Backpack - 35L at $69

I want to get this one

http://www.amazon.com/Plano-Guide-Series-Polycarbonate-Field/dp/B003JFU652/ref=sr_1_6?s=sporting-goods&ie=UTF8&qid=1371432662&sr=1-6&keywords=plano+waterproof

If you are handy you can get a cheap water tight case and do your LED idea in it. Heck, you could get a case and a multi LED light.

http://www.amazon.com/Plano-Guide-Series-Polycarbonate-Field/dp/B003JFU652/ref=sr_1_6?ie=UTF8&qid=1367598398&sr=8-6&keywords=PLANO+WAterproof

http://www.amazon.com/27-LED-Super-Bright-Magnetic/dp/B003377UIC/ref=sr_1_16?ie=UTF8&qid=1367598427&sr=8-16&keywords=LED+Light

I have this one. Fits shoes, towel, full outfit, etc. Has a mesh pocket on the bottom to put your wet swimsuit if you don't want it getting your clothes wet. The side pockets are also big enough for shoes.

I'm 6'1 with size 12-13 shoe.

OH and there's a laptop sleeve if you need a full commuter bag.

EDIT: Laptop sleeve.

This may meet your bag criteria, I own a couple of them. I have one for a gym bag, one for traveling, and one for emergency pack.

heres some extra stuff i pack in my bag

• lots of tape
  
• extra belt, underwear and change of shirt
  
• surgical scissors to quickly cut the tape off after sessions
  
• kneepads / shin guards for spazzy white belts
  
• this mesh bag to dump my sweaty gi, gear and clothes in after a session so it can breathe on the way home.
  
• tiger balm and some muay thai liniment I use for my shins from cross training muay thai. (also for training through sore muscles, I use this sparingly though)
  
• mouth guard
  
• gatorade powder
  
• towel to wipe down afterwards / lay on my car seat