This paper addresses a problem of location parameter estimation from multibit quantized measurements. An adaptive estimation algorithm using an adjustable quantizer is proposed. By using general results from adaptive algorithms theory, the asymptotic estimation performance is obtained and optimized through the quantizer parameters. Despite its very low complexity, it can be shown that the proposed algorithm is asymptotically optimal for estimating a constant parameter. The asymptotic performance for optimal quantizer parameters is shown to rapidly reach real-valued based estimation performance as the number of bits increases. In practice, 4-bit quantization appears to be enough for estimation purposes. It is also shown that the performance gap between the quantized and continuous cases is even smaller when the parameter varies according to a random walk (Discrete Wiener process with or without drift).