Close to the ground you have the Murrayfield Hotel and Hampton Hotel on Corstorphine Road. Further east, between the ground and the city on Wester Coates you'll find a wide selection of hotels and guesthouses.
Further afield, if you're looking for a little luxury then try the original Malmaison in Leith, The Glasshouse, The Balmoral or The Caledonian. All these hotels will offer you an amazing experience. However, if you fancy something a little less swish, Edinburgh has loads of hotels, guest houses and hostels to suit all tastes and wallets. There are also a great many online hotel guides and booking services; I recommend HotelReview™ Scotland and Visit Scotland.