Here is a list of--in my opinion--the five best places to submit a science fiction short story. The picks are not ranked in any particular order. If you'd like to point out a magazine not mentioned, that's great--leave it as a comment.
Also, I'd suggest that if you haven't already, pick up a copy of the "Writer's Market," a writing reference book categorizing thousands of book publishers, magazines, journals, agents, etc. I consider it very useful and have used it for this list.
Here we go:
1. L. Ron Hubbard's Writers of the Future Contest (www.writersofthefuture.com)
Info: Quarterly contest; winning stories are published yearly as a collection.
Word count: up to 17,000.
Pay: First place: $1,000; second place: $750; third place: $500; $5,000 grand prize for best of the year.
Response time: More than three months.
About: This is a prestigious short story contest for new writers. I think it's one of the best contests for speculative fiction. If you can win this contest, you're one of the best.
2. Lightspeed (www.lightspeedmagazine.com)
Info: Monthly online magazine (started this year)
Word count: 1,000–7,500.
Pay: 5 cents/word for short stories.
Response time: Two days to two weeks (really great).
About: I recently discovered this magazine and love it! The website is well-designed and the stories are excellent. Stories are posted online for free, but you can buy a downloadable issue for $2.99. I'm confident the magazine will go far.
3. Analog Science Fiction and Fact (www.analogsf.com)
Info: Monthly magazine; accepted stories are published about 10 months later.
Word count: under 7,500.
Pay: 6-8 cents/word for short stories.
Response time: A few months.
About: This magazine is science- and technology-oriented. They have some great stories focused on technology.
4. Asimov's Science Fiction (www.asimovs.com)
Info: Monthly magazine (with the exception of double issues); publishes accepted stories 6-12 months later.
Word count: 750-15,000 for short stories.
Pay: 5-8 cents/word for short stories.
Response time: Three months for stories; two months for queries.
About: You should to have character-oriented stories for this magazine. The magazine accepts some new writers.
5. The Magazine of Fantasy & Science Fiction (www.fandsf.com)
Info: Bimonthly magazine; publishes stories about 6-8 months after acceptance.
Word count: less than 25,000.
Pay: 6-9 cents/word for short stories.
Response time: Less than two months.
About: The magazine prefers character-oriented stories. It also accepts poetry.