Since this is a question about a tattoo, I'd recommend against anything other than Kanji, unless you guys have a specific preference towards Kana's. That said, let's examine the options:

Kanji term 永遠 is literally the one-to-one translation of "forever," and no you do not add the に. Adding に would make it an adverb, and is required for grammatical functions, but there is no reason to include a grammatical particle in a tattoo. 永遠 is usually read as "ei-en", but in songs and poems the same Kanji can be read as "to-wa" as well, meaning the same thing.

永遠な愛 Everlasting love (love that is forever)
永遠に続く To continue forever.

The な and に are grammatical particles I do not suggest you include.

Another possible word is 永久, meaning "eternal" or "forever" as well, but it sound more formal and are used in more serious, less poetic, less literary situations. It's read as 'ei-kyuu'

永久保証 Life-time guarantee(eternal guarantee)
永久脱毛 Complete hair removal (hair removed forever)

Then comes your hiragana options: ずっと means something very close to "always", and is a very common word in speech that does not carry the artfulness nor the poetic-ness of 永遠. It's just a plain word to anyone who speaks Japanese, and frankly, a tattoo that says only ずっと and nothing else doesn't make much sense. It's almost as random as someone getting an English tattoo that says "blue".

いつまでも literally translates to "until whenever", and is better than the former option. It's used in a lot of art works, and seeing this phrase(not a single word) on its own as a tattoo is not so out-of-place. There are actually songs titled "いつまでも" so it's a good one if you prefer the look of the characters.

One more option, you could use the Hiragana とわ (to-wa) if you'd like, as that's probably the most literary, poetic way to say "forever" in Japanese among these options. To-wa could also be written with the Kanji 永遠 and 永久, but conversely when people see 永遠 and 永久 the first reading that comes to mind is "ei-en" and "ei-kyuu", unless they're told to read it as "to-wa". So, if "to-wa" is what you want, it's better to render it in Hiragana as とわ to avoid mis-readings. It all comes down to personal preferences.