Links to various level editors, moddable games, engines, and art tools
It's difficult for us to recommend level design tools. AAA studios do not release (or support) public SDKs anymore, while indie devs rarely have the resources to support public tools either. What's left is decades old, from an ancient golden age. We live in a fallen world.
Nevertheless, this page contains several lists of links to useful tools, both ancient and modern:
Moddable games (recommended). A short list of moddable games suitable for "serious" level design, where you will find active level design community who can help and support you.
Moddable games (all). A more comprehensive list of known games with modding tools. However there may be zero info or support, or popular games may not be regarded as "real" level design. (For example, Fortnite and Roblox are massively popular games with creation tools, but outside of these communities, you likely won't get work as a level designer with a Roblox portfolio.)
In the end, the best tool is whatever you will be motivated to use consistently.
screenshot of Godot v3.0, rapidly emerging as a popular free and open source community alternative to Unity and Unreal
2D level editors
If your engine already has a built-in 2D level editor, then use that. But if you're using a homemade engine or web-based framework, you'll need a standalone 2D level editor.
Unlike the fragmented 3D editor ecosystem, all standalone 2D level editors are open-source, stable, and engine-agnostic with easily parsed JSON file formats. Here we generally recommend Tiled, with its many features and widespread engine support.
screenshot of Tiled, a free open source standalone 2D tile-based level editor
3D art tools
In most cases, we don't recommend using 3D modeling tools to build levels. That said, all these tools basically do the same thing, and you should use whatever tools you like using.
We generally recommend Blender, free open source software that now rivals commercial tools. Older artists often prefer Maya or 3DS Max because they already learned it + industry pipelines are tightly coupled. But let's be clear -- Blender is basically the future, and Autodesk's days are numbered.