My favorite hotel in Florence (The Lungarno) is over there but it's expensive and I only stay there on a good deal (more likely off-season) and as we have a house in Tuscany we're only there for a night, maybe two. That said, when we've gone to Florence with friends where we're conscience of budget (we'll sometimes go with people visiting us) we've stayed at some other places. Both the Pitti Palace (right at the foot of the Ponte Vecchio) and Hotel La Scaletta are perfectly fine for a night (but not at the level of the Martelli 6 from the picture I saw). Since you're there for 4 nights, you definitely should stay at a place which has some luxe and pampering. While I have some hotel loyalty/preference I'm more loyal to my wallet so I generally shop for good value. There are a number of places in Oltarno I'd stay but only if there's a good deal to be had. Look around and price options. Realize a) Tripadvisor is not a reliable resource for hotels and restaurants in Italy (too many fake reviews) and b) some properties that look good in Florence have adjunct spaces and some of their better prices may put you in them.
Michelin lists some good hotels but you can try to price them outside of Michelin and often get a better price.