Niraj Chauhan

This plugin will help the user to add a drop-down-custom-taxonomy box with the help of small code on his desired location.
<h4>Options</h4>
just place this small code into your theme file and the drop-down box will appear on that page 
code: 
for example, if you want to display it on home page, 
then navigate to index.php, the inside that put this code, if you want to display the custom taxonomies, then just replace category with your custom taxonomy name.

Drop-down-taxonomy

This plugin will help the user to add a drop-down-custom-taxonomy box with the help of small code on his desired location.

sungraizfaryad

Remove Taxonomy URL strips the base slug (<code>/genre/</code>, <code>/topic/</code>, etc.) from your custom taxonomy term URLs so visitors and search engines see clean, short permalinks.
What 3.0 adds:
<ul>
<li>301 redirect old URLs — old <code>/taxonomy/term/</code> URLs redirect permanently to the new <code>/term/</code> URL so SEO equity is preserved when you turn the plugin on.</li>
<li>Hierarchical term URLs — nested taxonomies resolve correctly. <code>/parent/child/</code> reaches the child term instead of returning 404.</li>
<li>Pagination support — <code>/term/page/2/</code> works after the base slug is removed, no more pagination 404s.</li>
<li>Slug-collision detection — warns you (without blocking the save) when a term slug clashes with a page, post, or another taxonomy’s term, so you don’t accidentally break a URL.</li>
<li>Health Check tab — run a full audit of all selected taxonomies on demand.</li>
</ul>
All 3.0 features default to OFF on upgrade so your existing site behavior is preserved until you opt in.

Remove Taxonomy URL

Strip custom taxonomy slugs from URLs. Optional 301 redirects, hierarchical terms, pagination support, and slug-collision detection.

Drop-down-taxonomy vs Remove Taxonomy URL