Star Trek's "Space Seed" - 200 years in sublight stasis, no mention of speed or distance. Could be 0.5c for all we know. 100 ly at Enterprise's warp 6 cruising speed would take about 4 months, which seems not unreasonable.
The movie "Alien" - stasis, but seemingly with FTL given the times and distances involved. (https://avp.fandom.com/wiki/LV-223 says it was a 2 year voyage to the moon LV-223 in Prometheus.)
The TV series "Red Dwarf" - sublight, though it did break the light barrier once. Science in general is only relevant for comedic effect. https://www.ganymede.tv/2004/04/the-science-of-red-dwarf/ .
None of these seem to be characterized as "it takes you 150 years of travel at light speed to get to a place that is 150 light years away".
Which one am I missing?
It doesn't say if that's 120 ship years or Earth years. I'll assume ship years as that makes the most sense in context.
Assuming constant acceleration to the 1/2-way point, flip, deceleration, and using http://www.projectrho.com/public_html/rocket/slowerlight3.ph... :
T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)
60 years = (c / a) * arccos(a * 30 ly / (c^2) + 1)
1893456000.0 = (3E8/a) * arccos(a * 3.15576 + 1)
Using Wolfram Alpha to solve - https://www.wolframalpha.com/input/?i=1893456000.0+%3D+%283E... a = 0.14748 m/s^2 or about 1.5% g
Time elapsed on Earth is only a bit longer than ship time: t = (c/a) * Sinh[a*T/c] = 1.15 * ship time ("proper time")
Final velocity at flip is: v = c * Tanh[a*T/c] = 0.73 * speed of light