Choosing between a Post-Doc and a faculty position at "2nd-tier" institution
This depends on a number of personal factors. Here are some questions that I'd be asking in your situation:


How happy would you be with a career at the Tier 2 institute? Is this what you were aiming for, more or less, when you started your PhD? If so, then consider taking the job.
If you do a postdoc, how likely would you be to get a "better" academic job afterwards? And how much "better?" I wouldn't focus on the distinction between Tier 1 and Tier 2 so much; the characteristics of universities will differ greatly within each "tier". Here I'd ask the opinion of some senior scientists -- whoever wrote your recommendation letters, for example.
If you do a postdoc and don't get any academic job at all, how would you feel about this? If, for example, you would also enjoy an industry job, and those are widely available in your field, then you could consider taking on more risk.
Are there any personal factors at play? Are you eager to "settle down"? Do you have any responsibilities that require financial stability? Is the Tier 2 institute in a city where you'd enjoy living? If you do a postdoc, do you mind the prospect of moving again in a few years?


None of us on this website can answer any of these questions, but I suggest them as good questions to ask yourself. Best wishes to you!