A smartphone minus the cellular modem is just a PDA. Or rather, the modern smartphone could be viewed as the fusion of the PDA form factor and a cellular phone; this can be more clearly be seen in early smartphones like the Treo 650. Before then, it was common to have both as separate devices, and use Bluetooth (or even IRDA!) to connect both so that the PDA could use the cellular phone as a modem.

Unfortunately, like the current "smart TV" situation, it's going to be hard to find a PDA-like device without a built-in modem, since most people do want the built-in modem. There are tablets, but even them seem to be gaining built-in modems nowadays.

I got the Onyx Boox Palma for this. Phone-size E-ink screen (no SIM slot), Android + app store support under the hood.