「長生{ながい}きのために よく食{た}べることが大切{たいせつ}ですが、運動{うんどう}も本当{ほんとう}に大切{たいせつ}です。」
If you wanted as few corrections as possible, 「運動も本当に大切です」 could be left as is. While it is not completely natural-sounding, it could not be called incorrect, either.
When you list mutiple things in Japanese, however, it is ideal to put them in the same grammatical form. You used 「verb + こと」 for the first and 「noun only」 for the second.
Ideally, it should be either 「食べること」 and 「運動すること」 or 「食事」 and 「運動」.
The "real" problem with your sentence IMHO is actually the use of 「よく食べる」. This was obtained by directly translating "eat well", was it not? The truth is that 「よく食べる」 can only mean "eat a lot" in Japanese. A literal translation does not work here.
"To eat well" would be 「正{ただ}しい食事{しょくじ}をする」、「バランスの良{い}い食事をする」, etc.
Thus, the most natural way to list the two items would be:
1) Nouns: 「正しい食事」 and 「(適度{てきど}な)運動」
2) Verb + こと: 「正しい食事をすること」 and 「(適度に)運動すること」