5.7l 4x4. Where can I get a heater hose routing diagram?

I couldn't find a heater hose diagram specific to the 1999 Chevrolet Venture with rear heat and air, but I can give you the general location of the heater hoses and how to identify which ones go to the rear heat. The heater hoses on a 1999 Chevy Venture are located on the passenger side of the engine compartment. There are two heater hoses, one that is hot and one that is cold. The hot heater hose will be connected to the heater core, which is located under the dashboard. The cold heater hose will be connected to the engine. To identify which heater hose goes to the rear heat, you can look for the hose that is connected to the heater core outlet that is labeled "Rear Heat." The other heater hose will be connected to the heater core outlet that is labeled "Heating Core Inlet." Once you have identified the heater hoses that go to the rear heat, you can reconnect them to the heater core. Be sure to use new clamps when you reconnect the hoses. Here are the steps on how to replace the heater hoses on a 1999 Chevy Venture with rear heat and air: Disconnect the negative battery cable. Drain the coolant from the radiator. Remove the heater hoses from the engine and heater core. Install the new heater hoses. Fill the cooling system with coolant. Reconnect the battery cable. Start the engine and check for leaks.

You want to check the heater hoses going into the fire wall to the heater. 2 black water hoses from engine to cab. Once car warmed up, Both should be hot. If one hot and other cold, heater core clogged. If this is case, disconnect hoses from motor and Using water hose in heater hose flush heater core. Should come out rusty looking. Once water runs clear, push water through other hose to back flush. Once clear water seen, reconnect and top off antifreeze

not sure if this is what you are after but try this link..
Step 3: Connect the Hoses Together. Use a hose connector or hose coupler to attach the two ends of hose together. That way, the anti-freeze that would be routed through theheater core will instead just go through a short loop of tubing.

How to Bypass a Car Heater Core ' DoItYourself.com

www.doityourself.com/stry/how-to-bypass-a-car-heater-core How can bypass the heater core Google Search

Look at the fire wall you will see two hoses going through the wall they are 3/4 inch they will be your heater hoses one routes out the back of the intake manifold I believe the other is by the ECM valve.
Are you missing your heater hoses if so it may be that you have a bad heater core have you owned this car for long. If you are needing to reinstall all your hoses look on You Tube you will probably find a video telling you how to do it.

Google up "1999 Suburban heater hose diagram...

Yes they do appear to go to the same place but it isn't. Water comes out of the engine from one hose and returns to the engine on the other.
Attached link shows how to flush a heater core on a jeep. It doesn't really identify which hose is which but I would guess the the smaller hose comes from the engine and larger one returns it to the engine.
Because the water from the engine is under pressure and the return is under less pressure and larger to allow full flow.
2003 Jeep Liberty 3 7L Flushing the Heater Core

The second link shows the thermostat housing that the other ends of the hoses connect to.
How To Install Replace Engine Coolant Thermostat and Housing 3 7L 2002...

thier not much to route one hose come from the heat core to the engine and the other comes for the heater and goes to the heat valve and to the radiator.

You can unhook the hoses to the core and just hook them together with a flush fitting, or hose union.

1. Drain the engine coolant into a suitable container.
2. Open the instrument panel glove compartment. Push in on the sides of the compartment to release it, allowing access to the heater core.

The heater core can be damaged if too much force is applied to the heater core pipes during hose removal.

1. Remove the heater module screws and remove the heater module assembly cover. For vehicles equipped with A/C, remove the air conditioning evaporator temperature sensor assembly from the heater and A/C cover.
2. Remove the heater core screw and clamp.
3. Remove the hose pipe clamp screw and the hose pipe clamp. Clamp off the heater hoses.

Fig. 1: Heater hose and pipe routing-3.4L engine Fig. 2: Heater hose and pipe routing-3.8L engine Fig. 3: Heater hose and pipe routing-5.7L engine

1. Disconnect the heater hoses from the pipes.
2. Remove the heater core by carefully pulling it towards you.

Fig. 4: Exploded view of the heater core removed from the heater module assemblyTo install:

1. Install the heater core and attach the heater hose assembly to the heater hose pipes. Note the following:
   1. Lubricate the heater core pipes with petroleum jelly for ease of installation and to assure a good seal.
   2. Be sure the seals around the heater pipes remain in place when installing.
   3. To verify that the seal is installed correctly, observe the seal from inside the engine compartment. If the seal has leaks, apply a sealer between the heater core pipes and the evaporator housing.
2. Install the hose pipe clamp and the bolt/screw. Unclamp the heater hoses. Tighten the hose pipe clamp bolt/screw to 16 inch lbs. (1.8 Nm).
3. Install the heater core clamp and screw. Tighten the screw to 16 inch lbs. (1.8 Nm).
4. Install the heater module assembly cover and secure with the retaining screws. Tighten the screws to 18 inch lbs. (2 Nm).
5. Connect the negative battery cable.
6. Refill the cooling system. Operate the engine and check for leaks, add coolant if necessary.
7. Install the instrument panel glove compartment.

Make sure that you have 2 heater hoses going into the dash. These are 5/8" hoses coming from the water pump and going into the top of the engine. The 2 hoses go through the firewall into the heater core. If you don't have the 2 hoses going to the heater core, the previous owner may have it routing itself back to the engine. It the hoses are routed back to the engine, there's a chance of the heater core being bad as well and this is why it's by-passed.