A 20-amp outlet itself will not draw more power than a 15-amp outlet. Power draw is set by the active device plugged in, not by the outlet.
Ideally, on any circuit three items need to be matched. The breaker in the panel fixes the maximum current allowed in the circuit. The wiring from breaker to wall outlet(s) must be the correct size to carry safely the max current the breaker allows. The outlet fixture mounted in the wall box must have slots designed for a circuit of that capacity. This latter point ensures that you cannot plug a light-draw device with light-current wiring into a heavy-current source and risk having a malfunction that pulls heavy current that damages the connected light-duty device, but still does not overload and trip the breaker. It also ensures you don't try to plug a heavy current user device into a light-current circuit. (Of course, in this last case there is no big safety issue - the breaker will just trip!)
SO, ideally if you have a 15-amp or less load to plug in, the wall outlet should have its blade slots designed to match that 15-amp plug, and the wiring and breaker on the circuit should also be 15 amps. Now, realistically, most circuits are wired with several outlets on one circuit and breaker, so the TOTAL of all loads plugged in (not just of one of the load devices) is what is important. If you truly have a 20-amp device, it should have a different plug blade design, and that requires the correct outlet, wiring and breaker for the circuit.
Where I live, 15- and 20-amp circuits are set up with different outlets (blade designs). But in many part of the USA the electrical code allows the installation of a type of outlet fixture that has two-way slots - the slots will accommodate Either the 15-amp or the 20-amp standard blade configuration. For circuits installed this way, the wiring and the panel breaker have to be rated for 20 amps. This makes it practical to use only one or two heavy current users on this one circuit, or to use many smaller-current devices in many outlets. On such a circuit, it certainly should be acceptable to install a 15-amp outlet in one of the wall boxes and plug into it a device (such as your TV) with the standard 15-amp plug on its cord. Unless your TV actually has the 20-amp plug on its cord, there is NO reason to install a 20-amp outlet or a two-way outlet, when you KNOW the only thing being plugged in there will have a 15-amp plug.
I get your concern that the 20-amp breaker may not be sufficient protection for a 15-amp outlet device. First let's remember that the actual current is whatever the load plugged in pulls - in this case, your new TV, which I'm sure will not exceed 15 amps. But that's for NORMAL operation, whereas problems are more likely to arise from abnormal conditions like a short inside the TV. A real short will pull current well over 20 amps and trip the breaker. The rare intermediate case of an abnormally heavy pull (say, 23 amps) that fails to trip the breaker quickly would put strain on the 15-amp outlet device. But one reason the electrical codes allow this sort of circuit installation is that the devices (like the 15-amp outlet) actually have a pretty good safety margin so that, although they are technically somewhat over their design specs, they still are not a safety hazard.
For pictures, check this website:
http://www.stayonline.com/reference-nema-straight-blade.aspx
Scroll down a little to the chart for "2-Pole, 3-Wire Grounding". In the first row for 125 Volt, "Standard" 15- and 20-amp Receptacles are the first and third drawings. See how the one in between with the T-Slot will allow use of both types of plugs? I'm guessing, though, that the plug on the end of your new TV's cord looks like the 15-amp variety.
Incidentally, the diagrams show that the U-shaped hole (plug prong) is always Ground, and also identifies the slot always connected to the White wire, which is power supply Neutral. The unmarked third prong (the smaller one on the left for the 15-amp design) is the Hot line.
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