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What is the total length of cable between the antenna and TV? RG-6 has no more than 6 dB loss per 100 feet. If you have 50 feet or less, and no splitter, don't expect an amplifier to make much difference.
Amplifiers do not (can not) 'pull' signal from an antenna or out of the air. Amplifiers are best located close to the antenna because they only overcome signal loss that occurs on the output side of the amplifier. To overcome loss in the cable and splitter, an amplifier must be positioned upstream of the cable or splitter. If located at the TV, the only impairment they can help with would be poor tuner noise figure.
If you opt for a preamp, a cool closet, as close to the antenna as possible sounds like the best location.
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