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I use Microsoft Street and Trips to plan my routes. It does a good job of finding the fastest route. It has another great feature in that you can can "Search on Live Search," for RV PARK or Campground and it will list all the parks or campground for any current view of the map. Great little tool for around 30 bucks at any SAM's.
I also use the "Motor Carriers Road Atlas," by Rand McNalley to check overpass heights.
Here's what Microsoft Street and Trips says to take: (Costs based on 10 MPG at $3.50 a gallon of Diesel)
Time Mile Instruction ---- For ---- Toward
Summary: 1592.2 miles (2 days, 7 hours, 29 minutes)
DAY 1
9:00 AM 0.0 Depart Mayville on E Main St (East) 0.3 mi
9:00 AM 0.3 Turn RIGHT (East) onto M-24 [E Ohmer Rd] 22.7 mi
9:26 AM 23.0 Take Ramp (RIGHT) onto I-69 81.5 mi I-69 / Flint
10:36 AM 104.5 At exit 97, take Ramp (RIGHT) onto I-69 134.2 mi I-69 / FT Wayne
11:38 AM 177.7 Entering Indiana
12:29 PM 238.7 At 96B, stay on I-69 [US-24] (South) 96.5 mi
Check your departure time; the next stop is in a different time zone.
1:51 PM 335.2 At exit 0, turn RIGHT onto Ramp 0.1 mi I-465
1:51 PM 335.3 Take Ramp (LEFT) onto I-465 [US-421] 7.2 mi I-465 / US-52 / US-421 / In-37
1:59 PM 342.6 At exit 44A, turn off onto Ramp 0.2 mi I-70 / Indianapolis / Columbus
1:59 PM 342.8 Take Ramp (RIGHT) onto I-70 6.0 mi I-70 / Indianapolis
2:06 PM 348.8 At exit 83B, turn LEFT onto Ramp 0.2 mi I-70 / I-65
2:06 PM 349.0 At exit 83A, take Ramp (LEFT) onto I-65 [I-70] 2.4 mi I-70 / I-65
2:09 PM 351.4 At exit 110B, take Ramp (RIGHT) onto I-70 138.9 mi I-70 / St. Louis
3:21 PM 432.3 Entering Illinois
4:09 PM 490.3 Merge onto I-57 [I-70] 59.4 mi
Check local time; this stop is in a different time zone.
5:00 PM 549.7 End of day
DAY 2
9:00 AM 549.7 Stay on I-57 126.0 mi
10:27 AM 653.6 Entering Missouri
10:46 AM 675.7 At exit 1A, take Ramp (RIGHT) onto I-55 131.4 mi I-55 / Memphis
11:42 AM 742.3 Entering Arkansas
12:37 PM 807.1 At exit 8, take Ramp (LEFT) onto I-40 123.7 mi I-40 / Little Rock
2:21 PM 930.8 At exit 153B, take Ramp (LEFT) onto I-30 [US-167] 146.7 mi I-30 / US-65 / US-67 / US-167 / Little Rock
4:22 PM 1073.9 Entering Texas
4:26 PM 1077.4 At exit 220A, turn RIGHT onto Ramp 0.5 mi US-59 / Houston
4:27 PM 1077.9 Road name changes to US-59 [Jarvis Pkwy] 3.4 mi
4:30 PM 1081.3 Take Ramp (RIGHT) onto S Bishop Rd 0.4 mi US-59 / Lake Dr / Leopard Dr
4:30 PM 1081.7 Bear RIGHT (South) onto Local road(s) 142 yds
4:30 PM 1081.8 Keep STRAIGHT onto US-59 [S Lake Dr] 21.2 mi
4:50 PM 1103.0 Keep RIGHT onto Local road(s) 0.1 mi
4:50 PM 1103.1 Bear RIGHT (West) onto US-59 [SR-77] 10.8 mi
5:00 PM 1113.9 End of day
DAY 3
9:00 AM 1113.9 Stay on US-59 60.5 mi
9:54 AM 1174.4 Turn LEFT to stay on US-59 32 yds
9:55 AM 1174.4 Keep STRAIGHT onto Ramp 0.2 mi US-59 / US-79
9:55 AM 1174.6 Road name changes to US-59 [US-79] 4.0 mi
9:58 AM 1178.6 Keep RIGHT onto Ramp 0.2 mi US-59 / Houston
9:59 AM 1178.8 Turn LEFT (South) onto US-59 [US-59 Bus] 14.4 mi
10:11 AM 1193.2 Keep RIGHT onto Ramp 0.3 mi US-84 / US-59 / Nacogdoches / Palestine
10:12 AM 1193.5 Bear RIGHT (West) onto US-59 [US-84] 40.1 mi
10:51 AM 1233.5 Keep STRAIGHT onto Ramp 0.2 mi US-59 / Lufkin / Houston
10:51 AM 1233.7 Take Ramp (RIGHT) onto US-59 [South St] 15.2 mi US-59
11:05 AM 1248.9 Keep RIGHT onto Ramp 0.2 mi US-59 / US-69 / TX-287-Loop / Houston / Beaumont
11:05 AM 1249.1 Road name changes to US-59 [US-69] 5.7 mi
11:11 AM 1254.8 Take Ramp (RIGHT) onto US-59 [S 1st St] 248.2 mi Houston
3:09 PM 1503.0 Road name changes to TX-91-Spur 1.0 mi US-77 / Refugio / Corpus Christi
3:10 PM 1504.0 Road name changes to US-77 70.7 mi
4:13 PM 1574.7 Take Ramp (LEFT) onto I-37 [US-77] 16.6 mi I-37 / US-77
4:27 PM 1591.3 At exit 1D, take Ramp (RIGHT) onto Antelope St [I-37 Access Rd] 0.5 mi Port Ave
4:28 PM 1591.8 Turn LEFT (East) onto SR-407 [I-37 Access Rd] 0.1 mi
4:28 PM 1591.9 Keep STRAIGHT onto SR-407 [Leopard St] 0.3 mi
4:29 PM 1592.2 Arrive Corpus Christi
SUMMARY
Driving distance: 1592.2 miles
Trip duration: 2 days, 7 hours, 29 minutes
Driving time: 23 hours, 29 minutes
Cost: $557.34
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Good luck.
Edited to reflect your route.
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