I just moved across the country from my mom, and here's what I do:

I text my mom every day, and call her most days. I make the call between when I leave work and when my bus arrives for me to go home, it's about a 10 minute period. She knows to be available at 6, and it gives me a daily chance to tell her about the stupid monotonous things like I would if I was home, and she gets to tell me about her most recent podcast, or what drama there is at her work, etc.

The texts are minimal-- for instance, this morning I texted her when I found out that I no longer had to take a day off to move because it was a paid holiday already. Not really too important, but it keeps you in each other's daily lives.

It's really knowing the minutae and the mundane in each others lives that keep you connected. Also the asking for advice thing is a good idea. Maybe send a package home now and then? A book you think she'd like if you see it, or an envelope with a magazine article that made you think of her. It doesn't have to be a huge effort, but she'll notice.