To provide results according to location, the user should give you access to it, otherwise, you are violating his privacy. So assuming that premise, the first thing that would happen on your app, if you go for the automatic option, wouldn't be showing results, but asking for permission to get the location.
Of course, we can assume that the user is using the app voluntarily and that he knows the conditions, risks, etc.
Offering results immediately sounds good from the perspective of the feeling or perception of dynamism of the app, not to mention that it may be what the user wants. But, what if the user is sitting on a coffee shop, close to a friends house looking for openings? Or in a train? Or in a bus?, Or checking the openings from another city to decide if he wants to move there? Or ... The first useful screen, apart of requesting the access to location would be useless, or slow due to circumstances that could be solved by giving him the chance to ask for what he wants.
Considering the last paragraph, offering a search option sounds much better because the user will have control over his privacy, can use the app without disclosing information and can decide quickly where to look for openings.
But there is an even better option; if you offer an introductory screen with both options, search or nearby openings, you are accomplishing both desires, yours and your partner's, not to mention that the user would have a much better experience.