It is certainly feasible to do this although you may not necessarily need to go to a 7200 platform. A lot depends on what you are replacing the 3660 for, ie. is it because it is EOS/EOL ?
Attached is a useful pdf that compares performance between router platforms, should give you some idea of what a comparative router would be.
I don't know of such a doc but the easiest way to view which cards are supported with which router is to go to the Product Page for the specific product. In case you're not sure how to get to those pages -
From Cisco homepage select "Products & Services" from along the bar at the top of the web page. From there select "Routers" and then select the router you are interested in. When that router page comes up scroll to the bottom and then choose the "Relevant Interfaces and Modules" link.
For a NM-8A/S, Table 8 in https://www.cisco.com/en/US/prod/collateral/routers/ps274/product_data_sheet09186a0080091b8b.html notes it's supported in both the 2800 and 3800 series, although both the 4 and 8 port versions are EOS. (The 16 port NM or HWIC variants appear still current.)
Don't believe any NM card supported in the 7200 series. Further, don't see a similar featured PA card for the 7200 series. (If true, likely because a 7200 isn't positioned as an access server or for low speed WAN aggregation.)
If you study Jon's reference, you'll see a 2811 or better offers performance equal or better than a 3660. Unless you need a large increase in performance, you might not need to jump into the 7200 series. If your existing 36x0 performance was alright, an 1800 series might suffice too.
If you need some info about replacing your 8-port serial, check this link out:
There are 3 types of 8-port serial for you to choose from.
Hope this helps.