Correct, spectacular to look at, and very, very popular.

What a Japanese person actually thinks
Bold and traditional. Slightly yakuza-adjacent in Japan because of irezumi conventions, though as a lone character far less so than a full dragon illustration.

Meaning

Literally: dragon
Actually: Dragon — the East Asian kind: a serpentine water deity, not a European fire-lizard.

Scores

Naturalness●●●●●

Standard. Note the simplified form 竜 is more common in everyday writing; 龍 is the traditional form and looks far better as a tattoo.

Coolness●●●●●

One of the most visually impressive characters in the language — 16 strokes of pure density. Docked for ubiquity, not quality.

Watch out

lowVisible traditional tattoos still bar you from many onsen, gyms and pools in Japan. That's true of any tattoo, but dragon imagery specifically reads as irezumi.
lowMake sure your artist uses 龍 and not 竜 if you want the traditional form — they are the same word, very different pictures.

On skin

龍

Orientation: vertical

Heavy brush, large. 16 strokes at small scale will blur into a black blob as the ink spreads. This character needs at least 8cm.