Unfortunately you can't get more than 60 results from the Google Places API; at least not without breaking the terms of service:
Unless you have received prior written
authorization from Google (or, as applicable, from the provider of
particular Content), you must not: (d) use the Products in a manner
that gives you or any other person access to mass downloads or bulk
feeds of any Content, including but not limited to numerical latitude
or longitude coordinates, imagery, and visible map data
Furthermore, as you can read here:
It's in large part a licensing issue. But it's also because the goal
of the Places API is not to facilitate scraping or aggregation of
Google Places data in the way you describe. Any application that does
so is almost certainly not compliant with the Google Maps or Google
Maps API Terms of Service, and is likely to be blocked from using the
API or other Google services at any time. The Places API is intended
to allow apps to offer their users a way to discover of identify
Places nearby. There is a practical limit to the number of search
results that a user will scan through and consider. I don't believe
it's necessary to offer users 200 results, and I suspect that doing so
would only serve to increase development of applications that scrape
Google Places data, without adding significant benefit or utility to
the types of apps the API is intended to serve, and that we wish to
encourage.
As a further reference, have also a look at this answer.