My recommendation is to not start the Host gift habit just yet, unless she has already done something really special for you, something you normally would not have gotten without her intervention. Once you start gifting, you'll feel obligated to do something every time, which is fine if she turns out to treat you really well each time.
Certainly it is up to you, though. She won't think anything less of you if you don't bring a gift, the first time or ever. But it doesn't hurt to do so.
Since she gave you her phone number, yes call her to meet up. Think of something you'd like in case she asks "Is there anything else I can do for you folks?" Be ready to say "We've heard of xxxx restaurant and were considering having dinner there. Do you know of this place?" She will likely offer a comp. Take it. Then at the end of your stay you can put a $25 gift card in a nice thank-you card addressed to her (be sure you sign it and include your players card #), leave it at the Host station.