People almost always underestimate the cooling required for the Peltier hot side.
Note that the max dT of a Peltier is specified at zero thermal power transfer. dT=60 degC means that if you maintain hot side at +60, your cold side will maintain at +0 only if it's completely isolated and not cooling anything.
If you actually want to cool something, practical dT is going to be somewhere between 20 and 30 degC. This tends to get you about half of the rated power - i.e., a "60W" Peltier will cool by 30W and heat by 90W. This would be hot side actively cooled at +30 degC, and cold side at about +0 degC. And removing 90W of heat without getting the device surface over 30 degC is the difficult part. A CPU cooler won't do it, it's designed to dissipate 90W while keeping CPU under about 60 degC.
You can cool something to room temperature just by using a heatsink at a room temperature, so if you are using a Peltier, you likely want to go below room temperature.
So I'm guesstimating you want to have your cool side at least below +10degC, possibly even colder. Let's say you want +5degC. This would mean the hot side cannot be allowed to heat to over about 35 degC!
This means, your heatsink design needs to have only about 10 degC temp rise (measured between the Peltier hot side and the ambient) - preferably even less! - to make any sense. This means ridiculously low thermal resistance numbers. This is a Peltier-specific problem - other things (semiconductors, CPUs, etc.) that require cooling are usually just fine with dT=50 degC between the ambient and the device. So to cool a 60W Peltier properly, you'd need a heatsinking solution typically used to cool "400-500W things".
Note that heatpipes and similar vapor phase change based cooling devices won't work - they all need certain dT to start working at all, the thermal resistance is not a linear function. Fine for things that can run at, say, 60 degC, like CPUs, but not OK for a Peltier hot side that you want to cool to almost room temp.
You are left with water cooling, or a well designed fan cooling with a massive heatsink with thick enough base for proper heat spreading (think about 15-20 mm for aluminium or 10mm for copper!), then a lot of fan-cooled fins on it. These behave fairly linearly, and oversized enough, can cool with very low dT.