i have some bitcoins that i want to exchange
but i want to use a reputable website
is there such a thing?
if by exchange you mean sell and take the fiat then the good options is localbitcoins.com which you can find local people accepting bitcoin in exchange for local currency. just check their reputation first.
if by exchange you mean trade, then there are a lot of options.
for trading/exchanging with fiat good options are kraken, bitfinex
for trading/exchanging with altcoins good options are poloniex, bittrex
check out coinmarketcap.com/exchanges/ for a list of all of them with coins they have listed.