Let me answer some of your questions and then I'll talk about some pitfalls with an example.
Could this confuse the user? Will he start looking for other places
on this map?
A map widget will not confuse a user. It will offer more clarity to the user on how to find your shop, look for things to do near your shop and other local facilities and hotspots. There are pros and cons, but the pros definitely outweigh the cons.
The user might be looking for an Italian restaurant near an Irish pub (so they can get smashed and then grab a pizza for dinner).
User might look for a pub near a bus stop or train station (to avoid driving)
User might look for a pub near a strip club (that's my Friday night in a nutshell)
User might look for an expensive pub near cheaper pubs to bar hop (that's my Saturday night in a nutshell)
Allowing them to look for nearby places is a great user experience in the above scenarios.
If the user is a prospective customer then they are going to visit your shop regardless of looking up other places. If they are not—well maybe your map helped the user spot something they were seeking, at the end of the day, you've satisfied the user's experience with your page. That's not bad for business since they found it for through your brand's page, they'll remember your brand name and how it helped them... that's free advertisement.
Will the user be expecting an actual map or a static image ?
In this day and age, a good interactive map is better than a static map (emphasis on the word good here). But if your users are app lovers as I am, then an Interactive map is a bad idea.
The static map is not inferior; for example: you could have a static image of the map showing your business with near-by landmarks and have a hyperlink that takes the user to a larger map or send a key value to an app or another page with more details on the map.
- An app user would prefer (and I personally support) static maps that show landmarks near the business/shop with the detailed address; so I can copy this information to my own map application and navigate to the business.
- The static image is my key to ensuring I have the right business since I can spot the street name and nearby landmarks.
Here's why I hate map widgets with an example,
I wanted to service my BH bike, and these guys had a good reputation for servicing pro bikes.
Business page with map widget, showing the marker at the wrong location.
Actual shop location is 3kms from where the pin is shown on their page. I had to call the shop to confirm this.
Their address SK9 3PE is in Handforth, but their map widget shows Wilmslow. This is because, there's a Rolls Royce showroom with the name Royals; and I didn't know this.
So, I used their widget, got lost, gave up after an hour and went to another service shop (also because I was frustrated and past the shop's open hours)
So do not casually drop a map widget or a static image, unless you've tested it on all popular platforms for consistency.
If you try to look for their shop on google maps using the address they've provided, it still takes you to the wrong shop.
Addresses and maps are Key to every shop or business. And customers will use your map widget to navigate to your shop.
I hope this answer will help you decide what's best for your business/shop/app/website