With my boys, I always said they could watch the equivalent of one movie (1.5-2 hours) of tv. It was the same time every day during summer from 2-4, which also kept them out of the worst of the day's heat.
As for the handheld "reading" devices, I would recommend setting a time every day during which you all read, including you. First, you'll be around to monitor to situation. Two, this sets a great example regarding the value of reading. Three, it will give you a much needed break! In my home, we call them read fests. They were a struggle to start but now the shout of "READ FEST" never fails to bring my boys running! And if they break the sanctity of read fest by playing illicit games, the device gets locked away and they can read the old fashioned way with a book from the library. Simple.
As for playing the devices the rest of the day, I would limit it to an hour a day. I know with my boys, any more than an hour a day was the equivalent of giving them a stupid pill and I had to deal with their inability to think, process and act appropriately for the rest of the day. No, thank you!
I would also encourage you to get a ton of board games. Scrabble, Monopoly, Risk, Clue, Battleship, Apples to Apples, Sorry, Pictionary, Trivial Pursuit (jr. level, if available). My boys spent many a summer happily playing these games with all the neighborhood kids. There were days where I had 8 or 9 kids yelling and screaming (in a good way) about who was going to buy Boardwalk or take over some continent in Risk. It was truly awesome to see all the games of my childhood entertain the next generation.
I know this was more than you asked for, but I hope it helps. This summer, I have one son getting ready to go to college and they other involved in all sorts of activities from soccer to golf to horseback riding. TV time won't be our issue; finding time to watch it will be!
Happy summer.