Here’s something I've been thinking about—overuse of the word that. The American Heritage explanation is a little formal, but you’ll get the idea. That is often unnecessary and drags down the sentence. Read the sentence aloud and see if it’s needed for clarity. Sometimes it is, sometimes it isn’t. If it can be eliminated or the sentence rewritten to be stronger without it, do it. Work through a sentence to improve it. If it’s merely a device to get her to town, number 3 is tight and gets the job done, but you might come up with a more effective version. If the scene is important to the story, showing more—something like the last line—may be the best. Also, the writer's personal style makes a difference.
1. She thought that she would go to town and look for a dress.
2. She thought she’d go to town and look for a dress.
3. She’d look for a dress in town.
4. The frayed cuffs on her sleeves embarrassed her. Maybe she should spring for a new dress before the interview. The decision cheered her, and she started for town with a spring in her step.
You can omit that in a relative clause when the subject of the clause is different from the word or phrase the clause refers to. Thus, you can say either the book that I was reading or the book I was reading. You can also omit that when it introduces a subordinate clause: I think we should try again. You should not omit that, however, when the subordinate clause begins with an adverbial phrase or anything other than the subject: She said that under no circumstances would she allow us to skip the meeting. The book argues that eventually the housing supply will increase. This last sentence would be ambiguous if that were omitted, since the adverb eventually could then be construed as modifying either argues or will increase.