I would like to walk rather than take a taxi.

[tufguy]

1) I would like to walk rather than take a taxi.

2) I would like to walk rather than taking a taxi.

Are both of these correct?

 

[Tarheel]

I think so. (Let's see what the others say.)

 

[tedmc]

Both are correct but #1 is preferred (parallelism).

 

[jutfrank]

I assume you simply want to state a preference, so say this:

I'd rather walk than take a taxi.

 

[emsr2d2]

And if you really want to use "to walk", use "I would prefer to walk than take a taxi".