So you've done your launch - what's next? If you're trying to arrange a poetry reading in order to raise your profile or sell books, several options are available. There's little point going it alone. The options below try to tap into existing publicity systems, which can help a lot.
If a nearby town has a venue running a series of readings, you can try open-mics to gain experience. You'll struggle to get an evening to yourself unless you've published a few books.
You could take advantage of some skill or interest of yours other than writing - if you work in a big establishment (a hospital for example), you might try to arrange a lunchtime meeting in your workplace. Publicity shouldn't be a problem.
There are Writers Groups in most cities (poetry groups are fewer). They tend to plan their programmes a year ahead and are used to having known authors, so don't expect them to welcome you in unreservedly. Unless you're famous you'll probably need to do more than just read - you could run a workshop or judge a competition. They often pay, but you might prefer to appear for free, telling them that you'll bring some books for sale. They'll handle the publicity.
Nowadays there are many Arts festivals and Writers/Poets festivals. Unless you've published several books you're unlikely to appear in the main programme. Some festivals (e.g. Kings Lynn) have fringe events, which might be more suitable. You'll have a better chance if you team up with others. Festivals have bookstalls, which can be useful, but the biggest advantage is that they'll handle the publicity. It will help if you've previously attended the festival (or other festivals). The festivals needn't be Arts-centred - organisers of festivals about Food, Cromwell, Gardening, etc might welcome the chance to offer something a little different. Contact the organisers as early as possible.
Publicity-wise it helps to have a reason for doing a reading - an anniversary, launch of a new group, etc. As a venue try a library or a bookshop - they'll both help with advertising (publicity will otherwise be a problem) and might offer their services free. If your town has a venue often used for poetry readings, you could try that. Again, teaming up will help improve the size of your audience. If you have a publisher you could find out if any fellow-authors live nearby. If you know a musician, you could ask them to do a half-time stint. The more performers there are, the more friends they'll bring, especially if nibbles are available.