A.,
I have an only child as well. When my son was about this age, I started a routine of 'quiet playtime' to ensure I got a break during the day.
I started slow and there are a couple components to this which made it work.
FIRST, I ensured I had a time of complete, undivided attention with my son immediately before the quiet playtime. This was often in the form of either a 'snack storytime' (he eats a snack, and I read to him) or playing with him for at least 15-20 minutes.
Then, I started using a timer and explained that he might play in his own room until the timer went ding. I started at about 15 minutes or so and worked up from there. It's important that they trust the timer *will* ding, which is why I started small and worked up very quickly. At four, a 40 minute quiet time is reasonable; much more and they will have a harder time with it. I had to work up to that 40 minutes over about 2-3 weeks, if I remember correctly.
Always praise them for staying in their room. Much like bedtime, if they pop out, take them back to their room with little conversation. "This is quiet playtime, I'll see you when the timer goes ding/beep" and go back to your business.
Some pointers: for kids who need help entertaining themselves, limit media to no more than 2 hours a day total (for video games on leap pad AND tv combined). As a preschool teacher, I did notice that kids who had more media exposure typically spent more time not knowing what to do.
Help her beforehand-- before the quiet time, gather up some things she might like to do on her own. Beading activities, lacing cards, washable markers and paper on a clipboard... whatever you think she can handle on her own. Help her, though, to get an idea of *what* she wants to do before you leave her alone.
Also, schedule playdates whenever you can during the summer. Fours often want to be social, so ask the daycare who she plays well with at school and see if you can make some connections that way. As the mom of an 'only', it is WORK to keep my son fully busy in a social way, but that was the choice I made in having just one.
Remember, too, that at daycare she has adults who are accessible to her most of the time and with other media, she more or less hasn't HAD to entertain herself. So do give her 10 minute chunks of "I need you to keep busy while I'm doing X" a couple times a day, and anytime there's something she can help with, include her, even if it's just moving the clothes from the washer to the dryer-- my son loves to do that with me. :)