How can I export object's field schema information to excel?

The best thing I came across is https://schemalister.herokuapp.com/. No installation required since it is hosted as a Heroku app.

There was a free App for such an export but unfortunately it seems reported broken and removed from public app exchange:

https://appexchange.salesforce.com/listingDetail?listingId=a0N300000018leZEAQ

Try it. If you get it to run, it provides you a nice list with type information, label, api name, length, etc

We have also developed an sumilar App to read the field schema information, but jet not released an without excel export at this time. If 'easy describe' won't be fixed, I'll consider to release our app as private managed package.

If you just need the Api-Names, use any of the mentioned dataloaders. I would recommend workbench https://workbench.developerforce.com/login.php . Make an export limited to 1 row. In excel delete the lone data row and preserve only the first header row containing your field names. In excel there is an function to covert columns in rows. Use it and you have your list.

An other dirty trick is: go to the setup and your object and then to your field list. Mark it, copy it and paste it to excel. Won't be perfect but could be a start.