first time solo traveller - HOW MUCH TO SPEND A DAY?

A lot depends on what you like to do. What types of activities do you want to do when there? How are you traveling?

jus normal sightseeing won't have much entertinment. I would enjoy simply walking around nd talking to locals. jus take cheap flights to Paris or Milan and then trains within italty and then fly back london

"Would 50-60 Euro a day be adequate?" For daily spending money, yes. But definitely not if that includes transportation and accommodation.

The Euro amount you cite may not be adequate if you intend to pay for lodging within that amount--especially in London and Rome.

Double that number is about the minimum, unless you do not eat several times a day. Yes it would be possible, but certainly not pleasant.

A good hostel in Rome is The Beehive. It is safe, clean, and near the Termini train station. In Florence, I liked Hostel Archi Rossi.

amazingrace, your budget sounds a little low. Do you plan to cook your own meals at the hostels? That will take time (shopping, preparation, cleanup) away from your travel experience. Also, due to the current economy, some cities have surcharges on restaurants and hotels (including hostels). London, Paris, and Venice are relatively pricey. I travel on a very tight budget myself (I like to turn money into more time), but it can get very monotonous having a slice of pizza for dinner every day. Check out some student-friendly guidebooks for ideas (Lonely Planet is good).

As a senior (61) first time solo traveller, I had a 17 day trip last year in Austria, Switzerland and So. Germany. Your locations are some more on the expensive side. I spent most of my time in Rick S. suggested lower budgeted pensions. Some were as cheap at 28 Euro and as high as 100 Euro in Munich (cheap as I could find during Oktoberfest). Food varied from picnic, Oktoberfest, to take out & to dinner & Mozart concert in Salzburg. I average around 50 Euro per day. If you just picnic you can get by for less. I am going to Italy this fall for 18 days(Venice, Florence, Tuscany, Sorrento, Rome) and plan on about $80-$140/ night. Food will probably be between $60 - $80 day, because I want to try more local food and wine. I make my reservations before I go. I don't want to have to waste time while I am there looking for a spot. As mentioned many times before use Rick's books, Airbnb, VBRO, & Trip Advisor for recommendations. Don't forget entry fees. When you go you want to make the most of your trip and see the sights.
Your trip is covering a lot of ground that adds cost and travel time, limiting what you can do at each location. You don't say how long the trip is. Consider reducing the sights.