How to use 4 pin Honeywell NBP Series Pressure Sensor give 1 pin analog output?
First and foremost, take a look at Honeywell's technical note (0008245-2-EN) on NPB serie sensors. This serie provides the most basic sensor, meaning «bare essential», that is to say, it has no offset compensation, no calibration, no temperature compensation and, last but not least, no conditioning amplifier...  Your schematic, provided it has a properly calculated gain (according to sensor's slope and Arduino's ADC input range) would perfectly work on a SPICE simulator but it lacks some refinements to have any chance of working in the real world (so called as analog).   

Firstly, as recommended by Honeywell's note, you should probably connect a 93.5k resistor on the sensor's supply side to make sure it's offset does not drive the sensor's output under the floor (ground level or 0V) if measured pressure is in the lower part of it's full range. Secondly, all opamps, sadly, have some annoying offset at their output and, unfortunatly, resistors are not born equal... 

As an example, to minimize offsets and gain errors, both R1's values should be close to within .1% (either by very carefull selection or by using expensive metal-film resistors). Bottom line: you need to add an offset compensation to (any) instrumentation amplifiers by connecting the lower end of R3 (on the ground side) to an ajustable voltage divider (potentiometer)... as illustrated in Honeywell's note. 

But, to be really frank with you, after much experimentation, I now believe that life is (arguably) too short to fiddle with such a «work intensive» design. Just take a look at FREESCALE's MPX4250 series integrated pressure sensors: temperature compensated, calibrated, offset trimmed and  CONDITIONNED output, all for the same cost as NPBs... I am now using one of these as a barometer (I get about 2V output at 1 atm (101kPa)) with excellent result. This MPX4250AP-ND sensor  is directly connected to the input of a  programmable amplifier (Gv = 1) feeding a  16bits ADC (both parts of a USB data acquisition front-end for a PC running a custom Labview application) Good luck! 

PS1: Do not be fooled by NPB's higher (advertised) accuracy: to get it right you would need an extremely accurate calibrated standard pressure (NBS?) to calibrate your sensor (to remove the offset error) and also consider that Arduino's ADC has only 10bits of (maximum theoretical) resolution (meaning less in real world, although you could improve it by oversampling ...)

PS2: I have absolutely no connection with FREESCALE, just an old retired engineer...