The Decision
What constitutes a "Good" school? Good for you, value added to you, success for you. It doesn't do you any good going to a school where you don't succeed.
Offers for acceptance and support can be made any time, even as early as December, although most of them come during March and April, with 15 April being the latest date for general offers. With any luck and some diligence it is likely that you will have more than one offer. Unfortunately, you may have an offer which specifies a response time before you get all your offers. life is tough. Some departments will grant extensions to the decision time deadline, but don't count on it. Sometimes you just have to make a choice.
You can also get offers after the first round of offers have been made. If a department hasn't yet filled its slots they may make offers well into the summer. Make your best decision, but don't agonize over it. If you are unhappy, then you can change schools without too much difficulty. Don't confuse unhappy with unsuccessful though. Your portability depends on your record.
updated: 13 Sep 07