LibGuides: UGS 302: Reading and Writing Contemporary American Poetry / Randall: Reviews of Poetry

A review is written at the time a work is released.

Think of a book review in much the same way as you think of a movie review. Reviews typically offer an opinion of a book’s quality or value rather than an in-depth analysis of the work, and tend to be shorter than literary criticism.

New York Times Book Review
Yes, you will likely hit a paywall, but you may enjoy the interface a bit more. After finding an article of interest, you can search for it by title on the library website or ask a librarian how to get access.
New York Review of Books
This literary magazine is a great place for reviews.
LA Review of Books
Another great place for poetry reviews.
The New Yorker
Yes, again, you may hit a paywall. Same advice as above for NYTimes.

Nexis Uni
Yes, we subscribe to newspapers with book reviews. The search interface is more complicated, but it's nice because it allows you to limit to reviews across newspapers. See screenshot below.
Academic Search Complete

Here's how to search Nexis Uni for reviews. You can open this image in a separate tab or window to view larger.

This is how you search for reviews in Academic Search Complete. I would select both book reviews and poetry reviews from the drop down. The database relies on many publications to label their sources and you can't be sure of consistency.