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The the exact distance between Vallayambalam and Trivandrum Central is not known to me. May be 5 - 6 kms. Not more than that .
The auto fare would come to 40 - 45 rs .
And regarding a better Logde near the trivandrum central , Hotel Chaitram seems to be good. There is even Hotel Highland . There are many other hotels in and around. But these two are better known.