If i understand you correctly you want to take your company, Company A, and integrate your application into third parties but you are unsure whether or not they have the capabilities.
If that is not correct feel free to clarify but I'll continue as if the above is correct.
Also, I don't know if your example is what you are trying to accomplish or if you are in a more regulated industry, say insurance, where your selection of vendors is limited. For example, maybe you need to pull credit score information.
Regardless, to integrate with these companies you'll need either an API or a data dump to accomplish what you need.
So lets go through some scenarios:
1) You want to integrate with weather.com. A quick google search doesn't really show weather.com having a developer exposed API (I might be wrong) but there are plenty of other options like
AccuWeather Enterprise API - AccuWeather Enterprise API Documentation[
^] or say
API | Weather Underground[
^]
For something like terminal5nyc, a quick google search shows that they probably don't have a developer exposed API that you can integrate with so you would need to contact this company directly.
2) What I'll call a more "enterprise" like integration would be where you need to pull Credit Score information for people or say, pull their accident/driving violation history. Something like this there are a small set of well known companies that provide these services but you'll have to research and decide what company meets your needs. These sort of enterprise-esque requirements typically do expose APIs for use by developers in creating custom applications but you'll pay a pretty penny to get it up and running (ex: you'll do set up fees, license fees in some cases, and then monthly minimum/transaction based fees).
So the short of it is, you need whatever companies you are talking to, to know if they have an API that your development team can integrate with. If they don't, the second question would be do they have a data dump they can provide (whether real time, nightly or monthly) where you access it via say...FTP and would import that data into your system.
If the companies you are talking to don't have the capabilities for either, you'll either need to look for alternative companies that can provide the same service or re-evaluate what it is you are trying to accomplish.
Edit:
Just saw my assumption is what you are trying to accomplish but i'll leave my comments about enterprise level APIs in as well.
So i didn't see terminal nyc offering an API but maybe you can look at some other ticket based sites (ticket master or whatever other companies/sites offer concert booking information) and see if they have API's that can be consumed by developers to build custom applications.
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