Where to publish a laboratory manual?
To a publisher
Publishing a laboratory manual for an undergraduate course is in some way similar to publishing a textbook, which in some ways similar to publishing any other book.
Publishers publish books. In some cases, when they expect that there is going to be  a profitable market, they pay authors for the books they publish, and in other cases authors (or some institutions) cover the costs and either hope that the books will sell in sufficient quantity or receive the books and distribute themselves. In your case, the latter situation is likely - if you'd want to publish that manual, someone (perhaps your university department) would have to cover the full costs of doing so and would get the published manuals to distribute to students and potentially other customers.
Your university may have a publisher subsidiary (it's not that uncommon) who are involved in publishing academic material, if so, it would be worth talking to them.
However, that generally won't be treated as a peer reviewed research publication; it's plausible that it even won't be peer reviewed at all.  Preparing and publishing educational material can get you some &quot;points&quot; in various academic evaluations, but that's a different category than peer reviewed papers with novel research.