Can you suggest some board/micro-controller which is capable of having minimum two DC motor, a 16 * 2 LCD module and a Bluetooth enabled chip so that it can communicate with a phone for instructions .....
No need for PM as other people with similar problems won't be able to see the solution. Let's keep it open.
I have already built an Robot which is controlled by a 3-axis Accelerometer but the drawbacks of this bot was it was not wireless [...]
If You already have a wired
acc controlled robot it means than You already have board/micro-controller to control it. Are You sure it is not suitable to accommodate "two DC motor, a 16 * 2 LCD module and a Bluetooth enabled chip"
There are many ways to run DC motors as there are many different motor controllers which require different microcontroller features to be present, hence different amount of pins. However, to run 2 DC motors using plain transistor H-bridge You need 4, dedicated for the task, I/O pins.
There are many different LCDs requiring different microcontroller features to be present. However to run common LCD such as HD44780
You need to have 6 or 10 (depending on which configuration You want to run it) dedicated I/O pins.
Not too sure about BlueTooth modules, but I suspect that commonly they use USART feature of a microntroller (TX and RX pins), so You need 2 pins that are marked TX and RX.