As I travelled alone I liked to stay at Hostels and meet up with fellow travelers, I would look at www.hostelworld.com
in advance of arriving and put a few places into my GPS. In Odessa I stayed at Antony's Home which was OK for me, it's very central has a gated courtyard which is good security for the bike and in early June there was not many staying there. One problem is accessing some Hostels as you have to either have a code to get in or phone them, in Antony's Home if the main gate is closed you can put your hand through an opening and reach the latch on the inside to open the door in the gate (don't tell anyone!). There's a lot of Hostels close by in that area. Regarding restaurants without a doubt all over Ukraine the best value for money is "Puzata Khata" there's one in Odessa and Lviv just Google the name. It's similar to a canteen with a massive display of food and you just help yourself or they cook it in front of you and then pay after, so there is no having to translate menus. The one in Odessa is on the sixth floor of the Europa shopping centre on Deribasivs ka vul. 21 which is the main tourist place where people strut about, also at one end is usualy where a load of local bikers hang out.
She didn't like having her picture taken!