Tek DSA601/602...
Seriously?
http://w140.com/tekwiki/wiki/DSA600
"FFT: complex, forward and reverse, max. 16384 points; windows: Rectangular, Bartlett, Hanning, Hamming, Blackman, Blackman-Harris..."
Tekwiki neglects to mention it but the 11K series also supports waveform math functions like differentiation and FFT magnitude *and* phase which together may be used to do vector network analysis using a step signal source. Averaging and filtering may be applied to the FFT instead of the time domain waveform. Math also allows the FFT magnitude display to be corrected for ENBW. The 11K series are the oldest DSOs that I know of which support these things.
They aren't. The LeCroy 9400A (which came out in 1985) supports these when soft option WP02 is installed, which allows advanced FFT up to 25kpts. The LeCroy 7200a modular scope (1989) should, too, although I don't know what the max FFT size is.
At some point I may still pick up one of these DSOs for the above but I would prefer a better option short of a new DSO that costs more than my car.
If you want to do some TDR stuff then there are quite a few low-cost options available. The LeCroy 9300 Series from the '90s supports the above features with the (now free) software options WP02 and WP03, while offering FFT up to 1Mpts. There are various models of the 9300 Series with different sample rates and bandwidths, most of which can be had for a few hundred dollars in working condition (although these days you can find the successor LC Series for similar money, with faster processing and FFT up to 8M).
Also, there are TDR options for the HP 54120A/B/D sampling scope mainframes, one up to 20Ghz and one up to 50Ghz (scope and TDR mainframe are called 54120T). The scope frames are cheap, however the TDR heads are not but with some patience you can find working examples of scope + head for <£1200.