I (29/m) just got a job offer which was lower than expected

As the title states, I just received a job offer that was a bit lower than expected. I wanted to get some feedback from more experienced redditors.

Background

I live in a major US city where I make about $75k per year at a large and well known company in my field, I don't receive a bonus. I am a marketing manager. I have frustrations at my company, and feel I'm fundamentally underpaid for the workload and my capabilities. I was recently promoted and given a title at the firm (better bonus structure). That being said, I like the people I work with and I like the city I'm in.

Recently a friend of mine living in a small city across the country told me his company was looking for a marketing director. They have previously operated without a marketing expert but as they are growing quickly they've realized they have a strong need for one. They flew me out to interview me and it went well. They seem excited to have a professional from a major city coming to help them.

The Issue

I asked for $75k-$85K from them, depending on the benefits. I also asked for $5K moving expenses to be covered by them. This is a pretty generous salary for the region I'm moving to, but it seemed fair given that I'm moving to a tiny town and leveraging my considerable experience in marketing for them. They will get a complete marketing dept. rebuild out of me with knowledge you simply can't find online. I'm a talented writer, solid art direction skills, and experience with client-facing sales roles, communication with press, etc. IE I'm the full package, despite my age.

I got the offer today and it was only for $70k + 5k for moving expenses.

The Question

My question is whether I should counter-offer. $70k is still a great salary for the area but I feel its leaving money on the table not to counter. That being said, the latest e-mail seemed to be implying that they really wanted me and felt this was a great opportunity and that I should really seize the day. It felt a bit like saying "this is a final offer" without actually saying that.

Would you counter-offer in my position? I was going to say I would prefer 75k firm.

TL;DR Small company in small city offering me a good salary for the area, my experience, etc. but I would really prefer higher given that I'm leaving my whole life behind to pursue the opportunity. Do I counter offer?