I can think of two scenes in particular, but my memory still needs a little more jogging (just like the rest of me). I know there's more than this.
There's a scene early on where Ripley is recuperating on the station. She's in a lovely park and finds out that her daughter lived a full life, but is already dead. I imagine this scene was shot to remind us/introduce us to the fact that Ripley had a daughter. She missed all of her child's life except the early years. It makes it much easier to understand why she bonded so strongly and quickly with Newt. She has the chance to do it over.
There's also a quick scene near the end, just before Ripley goes to rescue Newt. It's on the second drop ship from the Sulako. She and Hicks exchange first names (Ellen and Dwayne). Hicks tells her "Don't be long, Ellen."
It's sweet and I like it. But then again, I'm a sucker for mush. It's as much romance as you'll find in this film other than:
1) Hicks showing her how to use the pulse rifle,
2) Hicks giving her the locator,
3) and Hicks diving through a window to rescue Ripley and Newt from the face huggers (okay, now I'm just projecting).