The New Haven Review publishes fiction, nonfiction and poetry. They prefer submissions from writers with some connection to New Haven, though this is not mandatory. 
Response time: A few weeks to several months for prose; 2-4 months for poetry
Word count: No strict guidelines; 1,200 to several thousand for prose, 4-6 poems
Pay: At least $500 for prose, at least $25 per poem
Details here.