In the sentence “レジャーが目的で行く“ what does the で express here? Does に work here? I was trying to compare it to the 〜しに行く, like 勉強しに行く．I understand that 目的 is a noun so there is no ます form. What if I want to say “for the purpose of flower viewing”. Where 花見 can be both a noun and a verb? Do I say “花見をしに行く” or “花見が目的で行く”？
This で is "the te-form of だ". Since 目的 is a noun, you need a copula (だ). It's in the te-form to express "collateral situation". If you know how 歩いて学校へ行く ("go to school on foot") or ハサミを使って紙を切る ("cut paper using scissors") works, レジャーが目的で行く is constructed in the same way; レジャーが目的で describes how the following action (行く) is achieved.
You cannot say レジャーが目的に行く, but you can say レジャーを目的に行く, which uses the
In the case of 花見, you can say one of 花見をしに行く, 花見に行く, 花見を目的に行く, and 花見が目的で行く.