I want to limit the playback to the part that is visible on the screen no matter the zoom level. I went through all the preferences and can’t figure out how to do it. Any help? 
You can’t do that in any automatic way, if I interpret your question correctly, because the visible region will change with zoom level.
You can label particular regions which fit the visible area at particular zoom levels.
I assume you don’t mean, play but don’t scroll the screen? That is at “Update display while playing” in Tracks Preferences.
Perhaps you could explain what you are trying to do then we may be able to help more.
Gale
I am recording my LPs to my computer. I have zoomed in on an area around where there might be a click. I want to play only the area that is visible on the screen and if the click is in that area, zoom in a little further. I want to keep repeating this process until I have definitely found the click. The way it is working now is that when I click “play” it rolls the area of interest off the screen and I have to go through a lot of effort to get back to the area where the click is. I would prefer it to play the visible area and stop. And as I zoom closer, same thing: play only the visible area. That way I can home in on the exact click and use the pencil tool to fix it, or simply delete the several samples where the click is. Thanks. 
If you click and drag a selction from within the on-screen audio and then press Play then only the selcted audio will be played
As suggested earlier you may want tio creat a temporary range label - select audio and press Ctrl+B.
You may want to try using Timeline Quick Play or Scrubbing
see: http://manual.audacityteam.org/o/man/timeline.html#tqp
and: http://manual.audacityteam.org/o/man/scrubbing_and_seeking.html
There is a Tutorial in the Manual on Click & Pop removal: http://manual.audacityteam.org/o/man/tutorial_click_and_pop_removal_techniques.html
Hard to find clicks can sometimes be found more easily in Spectrogram view: http://manual.audacityteam.org/o/man/click_removal_using_the_spectrogram_view.html
And once you have foun d the click try using the Repair tool: http://manual.audacityteam.org/o/man/repair.html
Easiest of all and by far the quickest and most thorough is to invest in Brian Davies’ excellent ClickRepair software (I graduated to that from doing manual repairs like you)
See this sticky thread: https://forum.audacityteam.org/t/click-pop-removal-clickrepair-software/1933/1
If you have more than a few LPs to fix clicks on ClickRepair will be a good investment.
WC
I think as suggested you should use selections, because you will ultimately need a selection to process the click.
However if you don’t have a selection, disabling “Update display while playing” in Tracks preferences will prevent the scroll happening. If you don’t want to turn that preference off and the screen scrolls, stop playback then use LEFT arrow followed by RIGHT arrow, or RIGHT followed by LEFT. This centres the editing cursor in the visible area at the exact place you originally started from.
You can instead click SPACE three times, but then the editing cursor will be at the start of the visible area, which I don’t personally find helpful.
Gale
Thank you very much for the help. I think I can handle it now. OK, one more time, how do you mark this post “SOLVED”? It is solved for me but I can’t see where to mark it like that.
[Moderator note: Just add “[SOLVED]” to the subject line and one of the moderators will close it. ]