Can we leave bags at hotel before checking in?

Yes, most hotels will let you leave your luggage with them if your room is not ready.

just,

Most hotels will have a luggage storage area until the rooms have been serviced.

I normally plan my arrival in each city for the early afternoon, so that I don't have to deal with that. Using that method allows me to have breakfast at the hotel I'm departing from (that's important since I'm paying for it) and in most cases check into my new room straight away.

We have never found it a problem. We have also sometimes been lucky and allowed into our room hours before official check in, but we never count on it.

I often arrive in a city before check-in time and if the room is available the hotel will check me in early, if not I leave my bag and return later. I always call to confirm my arrival time, which they seem to appreciate. I don't know if that gets a room ready faster.

You can always leave your bags before check-in if the room is not ready, as long as you're staying in a hotel and not an apartment (another poster kept saying her "hotel" wouldn't allow this, and it turned out it was an apartment - very different scenario). Similarly, you can leave your bags after check-out, if you're catching a later flight or train.

The only place I've ever seen a charge for this is the EasyHotel chain, as it's part of their business model.

Do be ready to quickly remove the stuff you will need for the day before surrendering you luggage (camera, guidebooks, day bag, maps, etc). You may not have space in the hotel lobby to unpack the whole bag to get at these things.

If someone has checked out early and your hotel knows when you are coming, they may have your room ready when you arrive. But, as said above, you can never count on this.

Some train stations have bag check stations! They charge a fee though. Check out Rick's guide for more info specific to the cities you'll be in.