Yeah, several. I imagine your old Sidis are really road shoe, so the cleat (whatever it might be) stands proud of the shoe sole. So you walk along as if you are wearing high heels...but the heels are in the front. Awkward!
The solution is pretty simple. Switch to mountain bike pedals and mountain bike shoes. Mountain bike shoes have a recessed space for the cleats, with a raised sole around the cleat. So you can walk pretty comfortably in many situations. Theyre what I use when I bike tour, as during the day I often am on foot checking out short side trips or hunting for a decent cheeseburger in a town we pedal through.
I dont have any super-strong recommendations on what to get. Shimano SPD cleats are fine ($20). Tie them into a pair of Shimano MT32L shoes ($80). Or, take a look at the Sidi Gau shoes ($190). Theyre a little stiffer, with better fit and longer-lasting construction. For something that is more of a stealth shoe, the Keen Austins ($120) look more like street shoes than bike shoe. Yet they take any SPD cleat.
For the pedal, Shimanos M324s ($85) are finedouble-sided, durable, just about fool-proof.
There are other cleats/pedals out there. Crank Brothers' cleats/pedals are wildly popular. They're the ones with the "eggbeater" design, which makes them effectively four-sided. Very easy to clip into, but not quite the pedal platform of the Shimano, so maybe a bit less comfortable after a long day. I wear Shimanos when I tour, but my mountain bikes have Cranks Brothers on them. So that has been my decision.