I suppose you're looking for a web wallet. I hope you understand the risks of using those.
Anyway, the days of online wallets and exchanges giving no fees are pretty much over. Poloniex only gives a fee of 0.0001 BTC, but there have been a lot of complaints about slow withdrawals in the last couple of months.
As for online wallets, Coinbase and Xapo used to cover your transaction fees and let you send for free. Now Xapo is charging a fee just to
receive BTC as well as a fee to send it, and Coinbase wants you to pay fees as well.
You might be able to find some obscure gambling site that doesn't have fees, but frankly I think you'd be much better off just taking your coins into a wallet where you control the private keys. It's important on August 1st and it's important after that as well, not to mention that the risks of a site running off are pretty high compared to the low fees you actually have to pay.
You can always use a
transaction accelerator if you want.